5.1 Objective and scope of design
5.2 The basic design process
5.3 Computation of advance and intake opportunity time
5.4 Furrow irrigation flow rates, cutoff times, and field layouts
5.5 Border irrigation design
5.6 Basin irrigation design
5.7 Summary
The surface irrigation system should replenish the root zone reservoir efficiently and uniformly so that crop stress is avoided, and resources like energy, water, nutrient, and labour are conserved. The irrigation system might also be used to cool the atmosphere around sensitive fruit and vegetable crops, or to heat the atmosphere to prevent their damage by frost. An irrigation system must always be capable of leaching salts accumulating in the root zone. It may also be used to soften the soil for better cultivation or even to fertilize the field and spread insecticides.
The design procedures outlined in the following sections are based on a target application, Z_{req}, which equals the soil moisture extracted by the crop. It is in the final analysis a trial and error procedure by which a selection of lengths, slopes, field inflow rates and cutoff times can be made that will maximize application efficiency. Considerations such as erosion and water supply limitations will act as constraints on the design procedures. Many fields will require a subdivision to utilize optimally the total flow available. This remains a judgement that the designer is left to make after weighing all other factors that he feels are relevant to the successful operation of the system. Maximum application efficiencies, the implicit goal of design, will occur when the least watered areas of the field are just refilled. Deep percolation will be minimized by minimizing differences in intake opportunity time, and then terminating the inflow on time. Surface runoff is controlled or reused.
The design intake opportunity time is defined in the following way:
_{} (58)
where Z_{req} is the required infiltrated volume per unit length and per unit width (and is equal to the soil moisture deficit) and r_{req} is the design intake opportunity time. For most surface irrigated conditions, r_{req} should be as close as possible to the difference between the recession time at each point and the associated advance time.
An engineer may have an opportunity to design a surface irrigation system as part of a new irrigation project where surface methods have been selected or when the performance of an existing irrigation system requires improvement by redesign. In a new irrigation project, it is to be hoped that the surface irrigation system design is initiated after a great deal of irrigation engineering has already occurred. The selection of system configurations for the project is in fact an integral part of the project planning process. If a new or modified surface system is planned on lands already irrigated, the decision has presumably been based, at least partially, on the results of an evaluation at the existing site. In this case, the design is more easily accomplished because of the higher level of experience and data available.
In either case, the data required fall into six general categories (Walker and Skogerboe, 1987):
i. the nature of irrigation water supply in terms of the annual allotment, method of delivery and charge, discharge and duration, frequency of use and the quality of the water;ii. the topography of the land with particular emphasis on major slopes, undulations, locations of water delivery and surface drainage outlets;
iii. the physical and chemical characteristics of the soil, especially the infiltration characteristics, moistureholding capacities, salinity and internal drainage;
iv. the cropping pattern, its water requirements, and special considerations given to assure that the irrigation system is workable within the harvesting and cultivation schedule, germination period and the critical growth periods;
v. the marketing conditions in the area as well as the availability and skill of labour, maintenance and replacement services, funding for construction and operation, and energy, fertilizers, seeds, pesticides, etc.; and
vi. the cultural practices employed in the farming region especially where they may prohibit a specific element of the design or operation of the system.
The surface irrigation design process is a procedure matching the most desirable frequency and depth of irrigation and the capacity and availability of the water supply. This process can be divided into a preliminary design stage and a detailed design stage.
The operation of the system should offer enough flexibility to supply water to the crop in variable amounts and schedules that allow the irrigator some scope to manage soil moisture for maximum yields as well as water, labour and energy conservation.
Water may be supplied on a continuous or a rotational basis in which the flow rate and duration may be relatively fixed. In those cases, the flexibility in scheduling irrigation is limited to what each farmer or group of farmers can mutually agree upon within their command areas. At the preliminary design stage, the limits of the water supply in satisfying an optimal irrigation schedule should be evaluated.
The next step in the design process involves collecting and analysing local climatological, soil and cropping patterns to estimate the crop water demands. From this analysis the amount of water the system should supply through the season can be estimated. A tentative schedule can be produced by comparing the net crop demands with the capability of the water delivery system to supply water according to a variable schedule. Ondemand systems should have more flexibility than continuous or rotational water schedules which are often difficult to match to the crop demand. Whichever criterion (crop demand or water availability) governs the operating policy at the farm level, the information provided at this stage will define the limitations of the timing and depth of irrigations during the growing season.
The type of surface irrigation system selected for the farm should be carefully planned. Furrow systems are favoured in conditions of relatively high bidirectional slope, row crops, and small farm flows and applications. Border and basin systems are favoured in the flatter lands, large field discharges and larger depths of application during most irrigations. A great deal of management can be applied where flexibility in frequency and depth are possible.
The detailed design process involves determining the slope of the field, the furrow, border or basin discharge and duration, the location and sizing of headland structures and miscellaneous facilities; and the provision of surface drainage facilities either to collect tailwater for reuse or for disposal.
Land levelling can easily be the most expensive onfarm improvement made in preparation for irrigation. It is a prerequisite for the best performance of the surface system. Generally, the best land levelling strategy is to do as little as possible, i.e. to grade the field to a slope which involves minimum earth movement. Exceptions occur where other considerations dictate a change in the type of system, say, basin irrigation, and yield sufficient benefits to offset the added cost of land levelling.
If the field has a general slope in two directions, land levelling for a furrow irrigation system is usually based on a bestfit plane through the field elevations. This minimizes earth movement over the entire field and unless the slopes in the direction normal to the expected water flow are very large, terracing and benching would not be necessary.
A border must have a zero slope normal to the field water flow which will require terracing in all cases of cross slope. Thus, the border slope is usually the bestfit subplane or strip. Basins, of course, are generally 'dead' level, i.e. no slope in either direction. Thus, terracing is required in both directions. To the extent the basin is rectangular, its largest dimension should run along the field's smallest natural slope in order to minimize land levelling costs.
The detailed design process starts with and ends with land levelling computations. At the start, the field topography is evaluated to determine the general land slopes in the direction of expected water flow. This need not be the extensive evaluation that is needed to actually move the earth. In fact, the analysis outlined earlier under the subject of evaluation is sufficient. Using this information along with target application depths derived from an analysis of crop water requirements, the detailed design process moves to the selection of flow rates and their duration that maximize application efficiency, tempered however by a continual review of the practical matters involved in farming the field later. Field length becomes a design variable at this stage and again there is a philosophy the designer must consider. In mechanized farming and possibly in animal power as well, long rectangular fields are preferable to short square ones in most cases except paddy rice. This notion is based on the time required for implement turning and realignment. In a long field, this time can be substantially less and therefore a more efficient use of cultivation and harvesting implements is achieved.
The next step in detailed design is to reconcile the flows and times with the total flow and its duration allocated to the field from the water supply. On small fields, the total supply may provide a satisfactory coverage when used to irrigate the whole field simultaneously. However, the general situation is that fields must be broken into 'sets' and irrigated part by part, i.e. basin by basin, border by border, etc. These subdivisions or 'sets' must match the field and its water supply. Thus, with the subdivisions established, the final land levelling is undertaken.
Once the field dimensions and flow parameters have been formulated, the surface irrigation system must be described structurally. To apply the water, pipes or ditches with associated control elements must be sized for the field. If tailwater is permitted, means for removing these flows must be provided. Also, the designer should give attention to the operation of the system. Automation will be a key element of some systems. The treatment of these topics is not detailed since there are other technical manuals and literature already available for this purpose.
The design methodology used in the guide relies on the kinematicwave analysis for furrow and border advance and a fully hydrodynamic model for basin advance. These are transparent to the user of the guide, however, and further explanation for those interested can be found in Walker and Skogerboe (1987). Simple algebraic equations are used for depletion and recession. This guide has reduced the role of these hydraulic techniques to the advance phase to allow the User to participate more in the design process. The interested reader can refer to several references in the bibliography for other graphical techniques which extend beyond those given here, but as one does so, it becomes more important to understand the nature of the hydraulic assumptions.
The difference between an evaluation and a design is that data collected during an evaluation include inflows and outflows, flow geometry, length and slope of the field, soil moisture depletion and advance and recession rates. The infiltration characteristics of the field surface can then be deduced and the application efficiency and uniformity determined. Design procedures input infiltration functions (including their changes during the season), flow geometry, field slope and length, and determine the rates of advance and recession as well as the field performance levels for various combinations of inflow and cutoff times.
Two of the design computations are the same for all surface irrigation systems. These are the estimate of required intake opportunity time and the time required for the water to complete the advance phase. A stepbystep procedure for these computations will be given here and simply referenced as such in later paragraphs.
i. Computation of intake opportunity time
The basic mathematical model of infiltration utilized in the guide is the following:
Z = k r ^{a} + f_{o} r (15)
where Z is the accumulated intake in volume per unit length, m^{3}/m (per furrow or per unit width are implied), r is the intake opportunity time in min, a is the constant exponent, k is the constant coefficient m^{3}/min^{a}/m of length, and f_{o} is the basic intake rate, m^{3}/min/m of length. In order to express intake as a depth of application, Z must be divided by the unit width. For furrows, the unit width is the furrow spacing, w, while for borders and basins it is 1.0. Values of k, a, f_{o} and w along with the volume per unit length required to refill the root zone, Z_{req}, are design input data.
The design procedure requires that the intake opportunity time associated with Z_{req} be known. This time, represented by r_{req}, requires a nonlinear solution to Eq. 15. The simplest way to this solution is to plot Eq. 15 with the parameters being used in the design, such as the drawings in Figures 21 or 27. Another convenient method for those with programmable calculators or microcomputers is the NewtonRaphson procedure which is three simple steps as follows:
1. Make an initial estimate of r_{req} and label it T_{1};2. Compute a revised estimate of r_{req}, T_{2}:
_{} (59)3. Compare the values of the initial and revised estimates of r_{req} (T_{1} and T_{2}) by taking their absolute difference. If they are equal to each other or within an acceptable tolerance of about .5 minutes, the value of r_{req} is determined as the result. If they are not sufficiently equal in value, replace T_{1} by T_{2} and repeat steps 2 and 3.
ii. Computation of advance time
The time required for water to cover the field, the advance time, necessitates evaluation or at least approximation of the advance trajectory. The first step is to describe the flow crosssectional area. For furrows and borders this is Eq. 48 in which the crosssectional flow area, A_{o} in m^{2}, and the inlet discharge per furrow or per unit width, Q_{o}, in m^{3}/min. The parameters p_{1} and p_{2} are empirical shape coefficients as noted previously. For border systems p_{1} equals 1.0 and p_{2} is 1.67. For most furrow irrigated conditions, p_{2} will have a value ranging from 1.3 to 1.5. Fortunately, the furrow hydraulics are not too sensitive to variations in p_{2} and a value of 1.35 will usually be adequate. The value of p_{1} varies according to the size and shape of the furrow, usually in the range of .3 to .7. Figure 51 shows three typical furrow shapes and their corresponding p_{1} and p_{2} values.
Figure 51. Typical furrow shapes and their hydraulic sectional parameters
In a level slope condition, such as a basin, it is assumed that the friction slope is equal to the inlet depth, y_{o} in m, divided by the distance covered by water, x in m. This leads to the following expression for A_{o}:
_{} (60)
Note A_{o} increases continually during the advance phase and must therefore be calculated at each time step of each advance distance as well as each flow and resistance. For sloping field conditions, A_{o} is assumed to be constant unless the flow, slope or resistance changes.
The input data required for advance phase calculations are p_{1}, p_{2} field length (L), S_{o}, n and Q_{o}. This information can be used to solve for the time of advance, t_{L}, using either of two procedures: (1) the volume balance numerical approach; or (2) the graphical approach based on the advanced hydraulic models.
iii. Volume balance advance
For the volume balance numerical approach, Eq. 46 is used to describe the advance trajectory at two points: the end of the field and the halfway point. Equation 48 for the end of advance was written earlier as Eq. 50 and the halfway advance was written as Eq. 49.
Equation 50 contains two unknowns, t_{L} and r, which are related by Eq. 32. In order to solve them, a twopoint advance trajectory is defined in the following procedure:
1. The power advance exponent r typically has a value of 0.10.9. The first step is to make an initial estimate of its value and label this value r_{1}, usually setting r_{1} = 0.4 to 0.6 are good initial estimates. Then, a revised estimate of r is computed and compared below.2. Calculate the subsurface shape factor, s_{z}, from Eq. 47.
3. Calculate the time of advance, t_{L}, using the following NewtonRaphson procedure:
a. Assume an initial estimate of t_{L} as T_{1}T_{1} = 5 A_{o} L / Q_{o} (61)b. Compute a revised estimate of t_{L} (T_{2}) as
_{} (62)c. Compare the initial (T_{1}) and revised (T_{2}) estimates of t_{L}. If they are within about 0.5 minutes or less, the analysis proceeds to step 4. If they are not equal, let T_{1} = T_{2} and repeat steps b through c. It should be noted that if the inflow is insufficient to complete the advance phase in about 24 hours, the value of Q_{o} is too small or the value of L is too large and the design process should be restarted with revised values. This can be used to evaluate the feasibility of a flow value and to find the inflow.
4. Compute the time of advance to the field midpoint, t_{.5L}, using the same procedure as outlined in step 3. The halflength, .5L is substituted for L and t_{.5L} for t_{L} in Eq. 62. For level fields, the halflength and the flow area must be substituted. Equation 48 is used with L and .5L to find the appropriate values of A_{o}.
5. Compute a revised estimate of r as follows:
_{} (63)6. Compare the initial estimate, r_{1}, with the revised estimate, r_{2}. The differences between the two should be less than 0.0001. If they are equal, the procedure for finding t_{L} is concluded. If not, let r_{1} = r_{2} and repeat steps 26.
As an example of this series of calculations, suppose the advance time is wanted for a field with the following data:
Infiltration parameters 
a = 0.568 

k = 0.00324 m^{3}/min^{a}/m 

f_{o} = 0.000174 m^{3}/min/m 
inflow 
Q_{o} = 0.15 m^{3}/min 
slope 
S_{o} = 0.001 
length 
L = 200 m 
roughness 
n = 0.04 
hydraulic section 
p_{1} = 0.55 

p_{2} = 1.35 
1. set r_{1} = 0.62. _{}
3a. _{}
Note: If the field slope is zero, Eq. 60 would be used here for A_{o} and would use L in place of x._{}
3b. _{} = 146  (+75.67) = 70.33 minutes
3c. Error = ABS (T_{2}  T_{1}) = 75  70.33 = 4.67 minutes. Therefore, let T_{1} = 70.33 and repeat steps (3b and 3c).
3b. The second iteration yields T_{2} = 70.33  (+4.2) = 66.13 minutes. Step 3c error is now 4.2 minutes so T_{1} = 66.13 and steps 3b and 3c are repeated. At the end of another iteration the error is less than one minute and the value of t_{L} is found to be 66.07 minutes.
4. The time of advance to the field's halfway point is found by following the same steps as outlined above by substituting 0.5 * L = 100 metres for the length and t_{.5L} for the advance time to this distance. The result after two more iterations is 21.9 minutes.
Note: If the field's slope is zero, the computation of t_{.5L} must begin at Step 3a using L/2 for x.5. _{}
6. The error in the parameter r (.6  .6285) is greater than the acceptable tolerance so Steps 2 through 6 are repeated. The final advance time is 65 minutes.
As one easily finds, the numerical approach is justified only when one has at least a handheld programmable calculator or microcomputer.
vi. Graphical advance
The graphical approach involving Figures 52a  52f for furrows and borders and Figures 53a  53f for basins has been derived from computations using the kinematicwave and hydrodynamic simulation models summarized by Walker and Skogerboe (1987). These models are available from a number of sources, some commercially, and are not included herein.
Figure 53a. Dimensionless advance trajectories for basins having an infiltration exponent a = 0.2
Figure 53b. Dimensionless advance trajectories for basins having an infiltration exponent a = 0.3
Figure 53c. Dimensionless advance trajectories for basins having an infiltration exponent a = 0.4
Figure 53d. Dimensionless advance trajectories for basins having an infiltration exponent a = 0.5
Figure 53e. Dimensionless advance trajectories for basins having an infiltration exponent a = 0.6
Figure 53f. Dimensionless advance trajectories for basins having an infiltration exponent a = 0.7
The graphical procedure is as follows:
1. Define the infiltration parameters k, a, and f_{o} the field length L; the field slope S_{o}; the inlet discharge Q_{o}; surface roughness coefficient n; and the hydraulic section parameters p_{1} and p_{2}2. Compute the inlet flow area, A_{o} using Eq. 48 for furrows and borders and Eq. 60 for basins:
3. Compute the dimensionless parameter K*:
_{} (64)4. Compute the dimensionless parameter L*:
_{} (65)5. Enter the appropriate figures for values of the infiltration exponent, a, which bracket the design value, interpolate for the value of K*, and read the two values of _{}:
6. Compute the time of advance:
_{} (66)7. Average the two values to get t_{L} for the value of a used in the design.
As an example of using the graphical approach, suppose, as in the example of the numerical volume balance approach, the input data are as follows:
1.
Infiltration parameters 
a = 0.568 

k = 0.00324 m^{3}/min^{a}/m 

f_{o} = 0.000174 m^{3}/min/m 
inflow 
Q_{o} ^{=} 0.15 m^{3}/min 
slope 
S_{o} = 0.001 
length 
L = 200 m 
roughness 
n = 0.04 
hydraulic section 
p_{1} = 0.55 

p_{2} ^{=} 1.35 
2. _{}Note: If the field slope is zero, Eq. 60 would be used here for A_{o} and would use L in place of x.3. _{}
4. _{}
5. From Figure 52d, interpolating about 75 percent [log(2.3/1) / log(3/1) = .76] of the distance between curves K* = 1 and K* = 3 yields_{} = 0.54. From Figure 52e, the same process yields a _{} = 0.50 for an average of 0.52. The advance time is then estimated as:
_{}
Note the value using the volume balance numerical method yielded 65 minutes. Usually with careful interpolation the values of t_{L} found from the two methods will vary less than 5  10 percent.
v. Summary
The calculation of advance time is possibly the most important design step. At the beginning of the design process, this procedure is used to test whether or not the maximum flow will complete the advance phase within a prescribed time. Then it is used to find the minimum inlet discharge, and in the case of cutback or reuse systems to find the desired flow for the system operation. It is suggested that after the maximum inflow is determined and the associated t_{L} checked, the flow be incrementally decreased and additional values of t_{L} determined so that a relationship between flow and advance time can be established. At the end of this procedure, the minimum flow will also have been identified as that which fails to complete the advance phase in a set time, 24 hours for example. Finally, the t_{L} computation is used repeatedly in the search for the flow which maximizes the application efficiency.
5.4.1 Furrow design procedure for systems without cutback or reuse
5.4.2 Design procedure for furrow cutback systems
5.4.3 Design of furrow systems with tailwater reuse
5.4.4 Furrow irrigation design examples
There are three primary furrow designs:
i. furrow systems without cutback or tailwater reuse facilities;
ii. the cutback system; and
iii. the tailwater recirculation system.
These systems should be flexible to irrigate fields adequately in which the surface roughness and intake rates vary widely from irrigation to irrigation. The philosophy of design suggested in this guide is to evaluate flow rates and cutoff times for the first irrigation following planting or cultivation when roughness and intake are maximum and for the third or fourth irrigation when these conditions have been reduced by previous irrigations.
i. Input Data:
Description 
Parameter 
First irrigation infiltration 
a, k, and f_{o} 
Later irrigation infiltration 
a_{s}, k_{s} and f_{os} 
Field length, width, slope, roughness 
L, W_{f}, S_{m} and n 
Required application depth 
Z_{req} 
Furrow spacing and shape 
w, p_{1}, and p_{2} 
Soil erosive velocity 
V_{max} 
Water supply rate and duration 
Q_{T} and T_{T} 
Number of furrows 
N_{f} = W_{f}/W 
ii. The maximum flow velocity in furrows is suggested as about 810 m/min in erosive silt soils to about 13  15 m/min in the more stable clay and sandy soils. A maximum value of furrow inlet flow, Q_{max} m^{3}/min, that will fall within the maximum, V_{max}, is:
_{} (67)The value of Q_{o} should be adjusted so that the number of sets is an integer number, i.e. N_{f}Q_{o} should be an integer, but should not exceed Q_{max}.
iii. Compute the advance time, t_{L}.
iv. Compute the required intake opportunity time, r_{req}.
v. Compute time of cutoff, t_{co}, in min by neglecting depletion and recession:
t_{co} = r_{req} + t_{L} (68)
vi. Compute application efficiency, E_{a}:
_{} (69)
The application efficiency should be maximized subject to the limitation on erosive velocity, the availability and total discharge of the water supply, and other farming practices. The inflow should be reduced and the procedure repeated until a maximum E_{a} is determined.
Any procedure which attempts to maximize application efficiencies will determine the minimal waste tradeoff point between tailwater and deep percolation. Small values of inflow reduce tailwater losses but increase deep percolation losses. Large furrow flows advance over the field rapidly thereby providing the potential for greater application uniformity and less deep percolation, but also greater tailwater losses as the water flows from the field for a longer time.
One method of minimizing tailwater is to reduce the furrow inflow when the advance phase is completed. Most cutback systems are designed to operate in two concurrent sets, one advance phase set and one wetting or ponding; set. The advance phase and the wetting phase are both equal in duration to the required intake opportunity time. One of the most common cutback systems is that proposed by Garton (1966) and is illustrated in Figure 54. The head ditch is divided into a series of level bays with spires or other means of diverting water into the furrows. As is shown, the differences in bay elevations correspond to the head on the outlets needed to provide the desired advance phase flow and the wetting flow simultaneously.
The design procedure for the system illustrated in Figure 54 follows a sequence not entirely unlike that of the noncutback systems but with several points of additional concern. In addition to information describing the furrow geometry, infiltration characteristics, field slope and length, and the required application, it is also necessary to know the relationship between head ditch water level and the furrow inflow:
_{} (70)
where c_{1} and c_{2} are empirical coefficients, h is the head over the outlets, in m, and A is the outlet area in cm^{2}.
Figure 54. Schematic drawing of the furrow cutback system proposed by Garton (1966)
Elevation drawing showing the system of cutback furrow irrigation. In A, bay l is delivering the initial furrow flow. In B, the check dam has been removed from bay l, bay 2 is delivering the initial flow, and bay l is delivering the cutback furrow flow. In C, the check dam has been removed from bay 2, bay 3 is delivering the initial furrow flow, and bay 2 is delivering the cutback furrow flow, and bay l is shut off.
The first calculation can be the required intake opportunity time using the first of the common design computations. The design should provide an advance phase flow sufficient to allow t_{L} = r_{req}. Since this requirement is most likely to be a constraint under high intake conditions, the design advance flow for the first irrigation following a cultivation or planting should be the upper limit. This flow, of course, must be less than the maximum nonerosive flow. Thus, the second computation would be to compute the maximum flow from Equation 69.
An intermediate design computation can be made at this point. The advance time can be calculated using the maximum furrow inflow, Q_{max}. If t_{L} is less than r_{req}, a feasible cutback design is possible and the following procedures can be implemented. If the advance associated with the maximum flow is too long, then either the required application should be increased (at the risk of crop stress) or the field length shortened. It is usually better to reduce the field length and repeat these calculations.
When the design is shown to be within this constraint on flow, the next computation is to find the furrow advance discharge which just accomplishes an advance in t_{req} minutes. If the advance time for a range of inflows has been determined as suggested earlier, identifying this flow is accomplished by interpolation within the data. If this information has not been developed, it is necessary to do so at this point. The easiest method is to change Q_{o} iteratively until the associated advance time equals the required intake opportunity time.
The cutback flow following the advance phase must be sufficient to keep the furrow stream running along the entire length. Thus, some tailwater will be inevitable but should be minimized. Knowing that infiltration rates will decrease during the wetting period to values approaching the basic intake rate suggests a guideline for sizing the cutback flow:
Q_{cb} = b f_{o} t_{L} (71)
where b is a factor requiring some judgement to apply. It should probably be in the range of 1.1 to 1.5.
The application efficiency of the cutback system can be thus described as:
_{} (72)
Once the advance and recession phase flows have been determined, the next step is to organize the field system into subsets. The first irrigating set must accommodate the entire field supply. The number of furrows in this set is therefore:
N_{1} = Q_{T}/Q_{o} (73)
For the second set,
N_{2} = (Q_{T}  N_{1}Q_{cb})/Q_{o} (74)
and similarly,
N_{i} = (Q_{T}  N_{i1}Q_{cb})/Q_{o} (75)
The field must be divided into an integer number of subsets which may require some adjustment of Q_{T}, Q_{o}, or Q_{cb}. And, it should be noted that irrigation of the last two sets cannot be accomplished under a cutback regime without reducing the field inflow, Q_{T}, or allowing water to spill from the head ditch during the cutback phase on the last set.
To relieve the designer of a cumbersome trial and error proceduretrying to find the number of sets and the furrows per set that will work with various water supply rates, a suggested procedure is to fix the number of sets and compute the necessary field supply discharge.
This is a four step procedure:
i. Compute the cutback ratio for each of the field's infiltration conditions:CBR = Q_{cb}/Q_{o} (76)Select the largest value, and discard the other.
ii. Let k be the number of sets and compute the following product stream:
for k = 2 A_{2} =  CBR (77)for k > 2 _{} (78)
Then the number of furrows in the first set is:
N_{1} = N_{f}/(k + A) (79)iii. Calculate the number of furrows in each remaining set as:
for k = 2 N_{2} = N_{f}  N_{1}or,
for k > 2 N_{2} = (1  CBR)N_{1} (80)and,
set first value of B =  CBR_{} (81)
N_{j} = N_{1} (1 + B) (82)
iv. Steps ii and iii ensure that the field subdivides into an integer number of sets, but the field supply must vary according to the number of sets:
Q_{T} = N_{1}Q_{o} (83)Thus for a single specified Q_{o}, the designer can subdivide the field into several sets and choose the configuration that best suits the farm operation as a whole.
Before moving to the final design computation, the design of the head ditch, mention is made of using the cutback system under variable field conditions. Irrigations immediately after planting or cultivation will be generally higher than those encountered after the first irrigation. It will not be possible to alter the number of furrows irrigating per bay of the head ditch, so the inflow to the entire system must be adjusted. The design procedure outlined above is repeated for the appropriate value of Z_{req} and infiltration. Then, the system discharge is determined by Eq. 83.
For the system illustrated in Figure 54, the design of the head ditch involves the calculation of the relative bay elevations. From Eq. 71, the head over the outlets during the advance phase, ha, is:
_{} (84)
and during the wetting period phase, h_{w}, is:
_{} (85)
Thus, the elevational difference between bays is h_{a}  h_{w}. Each bay should be designed as a level channel section of length equal to the number of furrows per set times the furrow spacing. To accommodate the drop between bays, it is helpful if the field has a moderate crossslope.
The application efficiency of furrow irrigation systems can be greatly improved when tailwater can be captured and reused. The design of such a system is somewhat more complex than the procedure for traditional furrow and cutback systems because of the need to utilize two sources of water simultaneously.
The major complexity of reuse systems is the strategy for recirculating the tailwater One alternative is to pump the tailwater into the primary supply and then increase the number of operating furrows to utilize the additional flow. Or, tailwater can be used to irrigate separate sections of the field or even other fields. In any case the tailwater reservoir and pumping system need to be carefully controlled and coordinated with the primary water supply.
To illustrate the design strategy for reuse systems, a design procedure for a common configuration outlined by Walker and Skogerboe (1987) is presented. The reuse system shown schematically in Figure 55 is intended to capture tailwater from one set and combine it with the supply to a second set. A similar operating scenario prevails for each subsequent pair until the last set is irrigated when some of the tailwater must be either stored until the next irrigation, dumped into a wasteway, used elsewhere or used to finish the irrigation after the primary inflows have been shutoff.
Figure 55. Illustration of a typical reuse configuration
The total volume of tailwater recycled will be held to a constant volume equal to the runoff from the first set. The difference in tailwater volumes between the first and subsequent sets may be wasted. The recycled flow can thus be held constant to simplify the pumpback system and its operation.
The reuse system design procedure is as follows:
i. Input data are the same as for the cutback system.ii. Compute the required intake opportunity time, r_{req}, as outlined previously.
iii. Compute or interpolate the inlet discharge required to complete the advance phase in approximately 30 percent of r_{req}, correcting if necessary for nonerosive stream velocities. See the suggestion at the end of section 5.4.1.
iv. Compute the tailwater volume as follows:
1 The time of cutoff is:t_{co} = r_{req} + t_{L} (86)2. The infiltrated depths at field inlet and outlets are:
Z_{in} = kt_{co}^{a} + f_{o}t_{co} (87)3. A conservative estimate of the field runoff per furrow is:
_{} (88)where from Eq. 74 N_{f} = Q_{T}/Q_{o}.
v. Compute pumpback discharge, Q_{pb}:
Q_{pb} = V_{tw} / t_{co} (89)vi. Compute number of furrows in second or subsequent sets:
_{} (90)vii. The field should be in evenly divided sets which may require repetition of the procedure with a modified furrow discharge.
The Problem. Furrow irrigation designs are often needed either for new irrigation schemes or on existing projects where improvements are needed. Land consolidation has been carried out in a number of irrigation projects where implementation has included land reform policies and has resulted in field units amenable to furrow irrigation. Consider one such case where the new farm units have been organized around a 2 hectare block 200 m by 100 m. Flows of 30 litres per second are allocated to each block for 48 hours every 10 days. Initial field surveys showed that the fields needing first attention were comprised of a loam soil, sloped 0.8 percent over the 100 m direction and 0.1 percent over the 200 m direction. The furrows were placed on 0.5 m intervals across the 100 m direction (and running in the 200 m direction). The furrows were assumed to have a hydraulic section where p_{1} = 0.57 and p_{2} = 1.367.
During the evaluations noted, the infiltration functions characteristic of the field were divided into two relationships to describe the first irrigation following cultivations and then the subsequent irrigations. These relationships are:
Z = 0.00346 t ^{.388} + 0.000057 t (first irrigations)
and
Z = 0.0038 t ^{.327} + 0.000037 t (later irrigations)
The evaluation used a Manning coefficient of n = 0.04 for all analyses.
The crops expected were studied along with the local climate and it appeared that the best target depth of application, or Z_{req}, would be 8 cm. With 0.5 m furrow spacings, Z_{req} would be 0.04 m^{3}/m/furrow.
Water is in short supply so the project planners would like an estimate of the potential application efficiency with and without cutback and reuse.
Initial Design Calculations. With the design algorithm in mind but considered only as a guide, let the design process begin with the limitations on the design parameters. The first of these can be the maximum allowable flow in the furrow, Q_{max}. The soils are relatively stable so assume the maximum flow velocity could be as high as 13 m/min. Equation 67 in a previous section provides the means of evaluating the corresponding maximum flow rate:
_{} (67)_{}= 1.768 m^{3}/min (the total field inflow could be put in each furrow in this case)
The field is 100 m wide so that using a 0.5 m furrow spacing results in 100/.5= 200 furrows. The water supply of 30 l/s or 1.8 m^{3}/min would service 1.8/.104 = 17.31 furrows per set or the field would be divided into 200/17.31 = 11.56 sets (obviously impractical since the sets must be comprised of an integer number of furrows and the field needs to be subdivided into an integer number of sets). A practical upper limit on the number of sets is perhaps 10 consisting of 20 furrows each and having a maximum flow of 0.09 m^{3}/min. Beyond this 'upper limit' some of the following options also evenly divide the field:
Number of Sets 
Furrows Per Set 
Furrow Flow 
10 
20 
.09 
8 
25 
.072 
5 
45 
.045 
4 
50 
.036 
2 
100 
.018 
1 
200 
.009 
The second limitation on the design procedure is whether or not the flow will complete the advance phase in a reasonable time, say 24 hours. Particularly important in this regard is what minimum flow will complete the advance phase within this limit. If the maximum flow is too small to complete the advance, the furrow length must be reduced.
The second common design computation described in Section 5.3.1 provides the means of determining the time of advance t_{L} as a function of furrow inflow, Q_{o}. The maximum inflow can be used to calculate the minimum advance time, but since the minimum flow conditions are not known, the maximum advance time must be established by examining each flow. The computation of t_{L} for each Q_{o} can be accomplished with either method outlined and if undertaken yields the results given in the following table which are also plotted in Figure 56.
Sets 
Furrow Discharge 
Advance Time 

First Irrigation minutes 
Later Irrigations minutes 

10 
.09 
58.2 
* 
8 
.072 
72.6 
* 
5 
.045 
130.8 
101.4 
4 
.036 
184.2 
132.6 
2 
.018 
847.8 
379.2 
1 
.009 
* 
2390.4 
Figure 56. Example relationships between inflow rate and advance time
i. Design and layout for traditional furrow irrigation
There are now five configurations feasible for the initial field condition and six for the later conditions. The design question at this stage is which one leads to the optimal design. The answer is determined by computing the application efficiency for each alternative. First, the required intake opportunity time for each condition is determined using the procedure outlined in Section 5.3.1. For the first field r_{req} = 214 minutes. Similarly for the later applications, r_{req} = 371 minutes.
The application efficiency for each of the possible field configurations can now be computed. The results, shown in the table below, indicate that one good design is to divide the field into 4 individual subunits or sets of 50 furrows and utilize an inflow of 0.018 m^{3}/min per furrow during the first irrigations. The resulting application efficiency would be nearly 56 percent. Figure 57 imposes this layout on the field. Then during later irrigations two sets would be irrigated simultaneously so that each furrow would receive .018 m^{3}/min. The application efficiency of later irrigations would be about 59 percent.
Sets 
Q_{o} 
Z_{req} 
E_{a}, in Percent 

First Irrigations 
Later Irrigations 

10 
.09 
.04 
32.6 
** 
8 
.072 
" " 
38.6 
** 
5 
.045 
" " 
51.5 
37.7 
4 
.036 
" " 
55.7 
44.2 
2 
.018 
" " 
41.9 
59.3 
1 
.009 
" " 
** 
32.2 
Figure 57. Final traditional furrow design layout
The frequency and duration of each irrigation needs to be checked and then the headland facilities selected and designed. During the first irrigation, the field will require just more than 35 hours to complete the irrigation (the sum of r_{req} + t_{L} times the number of sets). The later watering will require 25 hours. If evapotranspiration rates were as high as .8 cm/day, the irrigation interval of 10 days waters the field well within these limits (Z_{req} divided by the crop use rate approximates the irrigation interval). Since the water supply is presumably controlled by an irrigation department, the design can be substantially hindered if the delivered flows are not as planned.
It may be useful to examine briefly the performance of this design. If the actual irrigations evolve as these design computations indicate, the farmer's irrigation pattern will waste about 44 percent of his water during first irrigations and about 40 percent during later irrigations. By today's standards, these losses are large and it may be costeffective to add cutback or reuse to the system to reduce these losses.
Field operations. The question that arises at this point in the design is how to implement and operate the system on the field. How will the irrigator know what flow rates are actually running into the furrows, what the actual soil moisture depletion is, or when to terminate the flow into one set of furrows and shift the field supply to another set?
There are several types of furrow irrigation systems but probably the most common are those that either use open watercourses at the head of the field and divert into furrows using spires or siphon tubes, or those that utilize aluminium or plastic gated pipe. The task of sizing these headland facilities will be noted in a later section. The problem at this point in the design is the means of accurate flow measurement and management.
If the design is to be carried forward to an actual operation, the inlet must be equipped with a flow measuring device like those noted in Section 3. Then the irrigator with some simple instructions from the designer can 'share' this flow among the appropriate number of furrows and achieve a reasonably good approximation of the optimal discharge. In some cases, the outlets to each furrow can be individually calibrated and regulated. For instance, the size of the siphon tubes or spires might be selected by the designer. The irrigator can then adjust the flow by regulating the heads and/or the openings.
In short, this phase of irrigation engineering is highly dependent on the experience and practicality of the engineer. There is no single 'best' way to do things. What works well in one locale, may not in another. The computational procedures and methods of field evaluation provide the best values of the parameters. The good design can only give the irrigator the opportunity to operate the system at or near optimal conditions.
ii. Design of a cutback system
There is another point which is hidden by the hydraulics of surface irrigation (which have been largely omitted from this guide). The movement of the water over the soil surface is very sensitive to the relative magnitude of the furrow discharge and the cumulative infiltration rates. Irrigation practices which modify the field inflow, such as cutback, may actually reduce the performance of the system. In more practical terms, if the advance rate is slowed to accommodate a cutback regime, the gains in efficiency derived from reduced tailwater may be more than offset by increases in deep percolation losses. The user of this guide might repeat the following cutback design example using data and field conditions for a lighter soil to illustrate this problem. As described earlier, the inherent limitation of the cutback design is that the advance phase and the wetting phase must have the same duration.
Initial design calculations. The initial design computations for the cutback system are fundamentally the same as outlined above. The r_{req} for the first irrigation is 214 minutes and for the subsequent irrigations it is 371 minutes. If the two set system is envisioned (one set in the advance phase and one in the wetting), the advance time and cutoff times for the first irrigation are respectively, t_{L} = r_{req} = 214 minutes and t_{co} = t_{L} + r_{req} = 428 minutes. For the subsequent irrigations, t_{L} = 371 minutes and t_{co} = 742 minutes.
The next computation is the maximum flow, Q_{max}. Since the field and furrow geometries have not changed, the value of Q_{max} = 1.768 m^{3}/min. Then it is necessary to compute the relationship between the inflow and the advance time. Rather than specifying a range of discharges and computing the associated advance times as above, the cutback design looks for a unique flow which yields the t_{L} already determined as 214 or 371 minutes. This may appear simpler to some and more difficult to others. It is in fact the same effort with a slightly different aspect. The details of the computations are already given in the calculations of the previous example. Reading from Figure 56 for the two conditions, one finds that the necessary furrow flow, Q_{o}, during the first irrigation would be about .0330 m^{3}/min and .0184 m^{3}/min for later irrigations.
It is worthwhile emphasizing that the time of advance, t_{L}, associated with a furrow inflow, Q_{o}, must be less than the required intake opportunity time, r_{req}, in order for the cutback scheme to operate properly. When the maximum flow, Q_{max}, results in an advance time greater than the value required for the system to work, the field length would have to be reduced or Z_{req} must be increased.
Field layout. Once the advance phase inflows are established, the field design or layout commences with an estimate of the cutback flow. The one important constraint on the cutback flow is that it should not be less than the intake along the furrow and cause dewatering at the downstream end. Equation 71 was given to assist the designer in avoiding this problem, but it is only a guideline. Thus, for the first irrigation the cutback flow must be at least:
Q_{cb} = 1.1 * .000057 * 200 = 0.0125 m^{3}/min
In other words, the flow can only be cutback from .0125 m^{3}/min to .033 m^{3}/min, or to 38% of the advance phase flow. In subsequent irrigations,
Q_{cb} = 1.1 * .000037 * 200 = 0.0081 m^{3}/min
which is a cutback of 43 percent of the advance flow.
There are several unique features of cutback systems that need to be considered at the design stage. Of particular concern is the fact that the number of furrows per set must vary over the field if the water supply rate, Q_{T}, is to be held constant during the irrigation. The number of furrows per set can only be the same if the field supply is varied for each change in sets across the field. This is usually difficult if the water supply is being supplied by an irrigation project. However, for furrow systems to utilize cutback, the field supply must be regulated from irrigation to irrigation. To illustrate this, let us develop a field layout for the irrigations. Utilizing Eqs. 7783, the following table can be developed for a variable field supply rate. The Q_{cb}/Q_{o} ratio is taken as .43 reflecting the constraint imposed by the later irrigations. This ratio must be the same for all irrigations.
No of Sets in Field 
Number of Furrow Per Set 
Q_{T} 
Q_{T} 

Set Number 

1 
2 
3 
4 
5 
6 
7 
8 
9 

4 
67 
38 
50 
45 





2.21 
1.27 
5 
54 
30 
41 
36 
39 




1.78 
0.99 
6 
46 
26 
35 
31 
32 
30 



1.51 
0.84 
7 
40 
22 
30 
27 
28 
27 
26 


1.32 
0.73 
8 
35 
19 
26 
23 
25 
24 
24 
24 

1.15 
0.64 
9 
31 
17 
23 
21 
22 
21 
22 
21 
22 
1.02 
0.57 
One can see that if the water supply capacity is limited to 1.8 m^{3}/min, the field must be divided into at least five sets to accommodate the first irrigation condition. The upper limit on the number of sets can be evaluated by examining the duration and frequency of the irrigations. The time of cutoff for each set during the first irrigation was determined previously as 7.1 hours (428 minutes). For the later irrigations, t_{co} = 12.4 hours (742 minutes). For a 5 set system, the total duration of the later irrigations is, 6 * 6.2 = 37.2 hrs or 1.6 days, assuming the irrigator will operate 24 hours per day. (Note that because two sets are irrigating simultaneously under cutback with the exception of the first and last sets, the duration of the irrigation on the field is the number of sets plus 1 times the advance or required intake opportunity time.) Thus, if the 48 hour availability constraint imposed in the problem outline is maintained, a cutback system for this field is only feasible in the 5 or 6 set configuration without changing the depth of water to be added during each irrigation. For the purpose of this example, let us suppose the water supply agency will deliver water to a 5 set system needed for the cutback regime.
Field implementation. For this example, the field outlets are to be spires with adjustable square slide gates having the following headdischarge characteristics:
Spile Size 
FullOpen Area 
Discharge Coefficient 
(mm) 
(cm^{2}) 

19 
3.61 
0.00114 
25 
6.25 
0.00136 
38 
14.44 
0.00145 
50 
25.00 
0.00169 
Note that Q_{o} = c A h ^{.5} where h is the head above the spire invert in cm, and Q_{o} is in units of m^{3}/min.
The change in elevation across the 100 m headland of the field is 0.008 * 100 = 80 cm which is sufficient for the system shown in Figure 54. To make the system work, the bays need to be constructed on a level slope. The transition between bays is accomplished with a drop equal to the difference in the head between the advance phase flows and the cutback flows. They are then operated irrigation to irrigation by controlling the gate openings. For example, if the 25 mm spires are selected, the advance phase head at the full opening is:
h = (.0330 / 6.25 / .00136)^{2} = 15.07 cm
and for the cutback phase:
h = (.0330 * .43 / 6.25 / .00136)^{2} = 2.79 cm
Thus, the elevation drop between the bays should be 15.07  2.79 = 12.28 cm. This will necessitate elevating the head ditch approximately 30 cm above the low end of the field and providing a drop to the furrows.
When irrigating the field later, the head on the gates will necessarily remain the same, but the openings must be reduced. For the advance phase,
A = .0184 / 15.07^{.5} / .00136 = 3.49 cm^{2} = 55.8% opening
and similarly for the later irrigations:
A = .0184 * .43 / 2.79^{.5} / .00136 = 3.48 cm^{2} = 55.7% opening
The operation is relatively simple so long as the total field inflow rate can be regulated to compensate for the lower infiltration during later irrigations. Figure 58 illustrates the alignment of the head ditch for this cutback example design.
Figure 58. Cutback example field and head ditch layout
The performance of this design is calculated as follows. For the first irrigation (Eq. 72):
_{}
and for the later irrigations:
_{}
Cutback, therefore, substantially improves the efficiency on this field over traditional methods.
iii. Design of furrow reuse systems
Another furrow irrigation option is to capture runoff in a small reservoir at the end of the field and either pump it back to the upper end to be used along with the primary supply or diverted to another field. The system envisioned for this reuse example will use the same head ditch configuration as the traditional or cutback system options already developed. The irrigator will introduce the canal water to the first set and collect the surface runoff from it. Then with initiation of the second set and subsequent sets, the water in the tailwater reservoir will be pumped to the head of the field and mixed with the canal supply. The field layout will be similar to the schematic system depicted in Figure 55.
Initial calculations. Initial calculations begin again with the required intake opportunity. These results were determined in the previous example:
r_{req} = 214 min during first irrigationsr_{req} = 371 min during later irrigations
The maximum allowable furrow flows are also the same, 1.768 m^{3}/min. A ruleofthumb states that the advance time for reuse systems should be about 30 percent of the required intake opportunity time. From Figure 56, the first irrigation flow should be .082 m^{3}/min which will yield an advance time of .3 * .214 min = 64 min. Similarly, for subsequent irrigations, an advance time of 112 min based on a flow of 0.042 m^{3}/min is selected. When the maximum nonerosive flow fails to meet the 30 percent rule, it is usually taken as the furrow flow and the rule is ignored.
The application efficiency and field layout under the reuse regime are computed as before. It is first necessary to compute the deep percolation ratio and the tailwater runoff ratio for the possible range of flows. The usual procedure is to compute the deep percolation ratio and then find the tailwater ratio as 100  E_{a}  DPR in percentages. As an example, the first irrigation analysis can be demonstrated. From the volume balance advance calculations or, if one prefers, the graphical approach, the time of advance to the furrow midpoint can be found as 25.9 min. From this information the values of p and r in Eq. 32 are 8.45 and .7595, respectively. Then using the power advance trajectory (Eq. 32) and the infiltration function, the distribution of applied depths can be described as in the following table.
Distance From Field Inlet 
Computed Opportunity Time ^{1} 
Computed Application ^{2} 
(m) 
(min) 
(m^{3}/m) 
0 
278.5 
0.0466 
20 
275.4 
0.0463 
40 
270.8 
0.0458 
60 
265.3 
0.0453 
100 
252.6 
0.0440 
120 
245.6 
0.0433 
140 
238.2 
0.0425 
160 
230.4 
0.0417 
180 
222.4 
0.0408 
200 
214.0 
0.0400 
^{1} t_{op} = t_{co}  t_{x}, t_{x} = (x/p) ^{1/}^{r}^{2} application = depth * furrow spacing/m of width
Using the trapezoidal integration of the applied water, the amount infiltrated over the field length is
_{}= 8.733 m^{3}/furrow
The required application is:
.08 m x .50 m * 200 m = 8 m^{3}/furrow
The total inflow to each furrow is:
.082 m^{3}/min * 278.5 min = 22.84 m^{3}/furrow
The deep percolation and runoff ratios are thus:
_{}TWR = 0 % (on the assumption that all is recycled)
And, the application efficiency for the first set is:
E_{a} = 100  3.2  0 = 96.8%
The runoff fraction is:
_{}
The volume of tailwater per furrow is:
0.612 * 22.84 = 14 m^{3}/furrow
It is obvious, or should be, that recycling 61 percent of the water applied to a field is going to be relatively costly. Consequently, a wider range of furrow flows needs to be examined along with their performance characteristics. For the later irrigations of this example, the figures are as follows: DPR = 3.3 percent and E_{a} = 96.7 percent.
The field configuration. The reuse system will collect the tailwater from the first set in the runoff reservoir and pump it back in the supply to the remaining sets. The pumpback system will operate continuously and will have some excess capacity in the reservoir even though the total runoff from subsequent sets will be greater.
The field layout can be found by trial and error or calculated. If the layout is calculated, one approach is to fix a furrow flow and determine the external supply that is needed. Using the design relations in Section 5.3 one can derive the following equation for the layout.
_{} (91)
in which Q_{T} is the flow rate of the external water supply needed for the system in m^{3}/min, N_{f} is the total number of furrows on the field, Q_{o} is the design furrow inflow in m^{3}/min, N_{s} is the number of sets in the field, and TWR is the runoff ratio associated with an inflow of Q_{o} m^{3}/min. During the first irrigation, a Q_{o} of 0.082 m^{3}/min satisfied the probable requirements.
Choosing six sets as the basic field subdivision, the number of furrows in the first set is:
N_{1} = Q_{T}/Q_{o} = 1.8/.082 = 22
For the first irrigation, the volume of the runoff reservoir must be:
V_{ro} = 14 m^{3}/furrow * 22 furrows = 308 m^{3}
Recalling that for a first irrigation condition, the time of cutoff is 278.5 minutes, the capacity of the pumpback system is therefore:
Q_{cb} = 308 m^{3}/278.5 min = 1.11 m^{3}/min
The number of furrows per set for the subsequent sets is:
_{} (92)
There are 200 furrows in the field. Five sets would contain 36 furrows; one set, the first, contains 22. This is 202 furrows so it is necessary to reduce one of the sets by two furrows.
Now the system must be configured for the later irrigating conditions. If the individual furrow inflows are set at .042 m^{3}/min, two sets can be irrigated simultaneously to have effectively a 3 set system, and, the number of furrows in the first is:
N_{1} = 1.8 / .042 = 43
The volume of the runoff reservoir needs to be 493 m^{3} and the capacity of the pumpback system must be 1.02 m^{3}/min. It will therefore not be necessary to regulate the pumpback system during the first irrigation to a value different than that for later irrigation. The runoff reservoir capacity, however, is governed by the later irrigation. The number of furrows in subsequent sets is 79. This layout adds up to 201 furrows so the number in the last set can be decreased to 78.
5.5.1 Design of openend border systems
5.5.2 Design of blockedend borders
5.5.3 An openend border design example
5.5.4 A blockedend border design example
With two exceptions, the design of borders involves the same procedure as that for furrow systems. The first difference is that while the depletion and recession phases are generally neglected in furrow design, both phases must be included for borders. The second difference is that the downstream end of a border may be dyked to prevent runoff. One simplification of border analyses is that the geometry of the flow is simpler because it can be treated as wide, plane flow. The values of p_{1} and p_{2} are always 1.0 and 1.67, respectively.
The first four design steps for openended borders are the same as those outlined under subsection 5.4.1 for traditional furrow systems: (1) assemble input data; (2) compute maximum flows per unit width; (3) compute advance time; and (4) compute the required intake opportunity time. Hart et al. (1980) also suggest computing a minimum flow, Q_{min}, based on a value that ensures adequate field spreading. This relationship is:
Q_{min} = 0.000357 L S_{o}^{.5} / n (93)
where Q_{min} is the minimum suggested unit discharge in m^{3}/min/m and L, S_{o}, and n are variables already defined. There will be substantially more water on the surface of borders than for furrows. Consequently, it is good practice to check periodically the depth of flow at the field inlet to ensure that depths do not exceed the dyke heights. For this:
_{} (94)
where y_{o} is the inlet flow depth in m.
The border designs given here assume the advance phase is completed before the inflow is terminated. Many irrigators, in fact nearly all where the downstream end is dyked, actually cut off the inflow before the end of the advance phase. In these cases, the volume of water on the surface will continue to advance along the border until it reaches the lower end where it will run off or pond in front of the dyke. Unless the border system is extremely well designed and operated, the downstream pond often creates a substantial threat to the crop in the submerged areas and although dyked at their lower ends, most farmers provide a surface drain for excess water. Consequently, the border efficiency and uniformity are approximately the same as borders in which excess surface water simply drains off the field after the advance phase is complete. The following procedure is therefore suggested for border systems where the excess surface water is drained from the field either by a completely openended border or by a regulated outlet from a blockedend border.
After completing the first four design steps, as with furrows, openended border design resumes as follows:
v. Compute the recession time, t_{r}, for the condition where the downstream end of the border receives the smallest application:t_{r} = r_{req} + t_{L} (95)vi. Calculate the depletion time, t_{d}, in min, as follows:
1. Assign an initial time to the depletion time, say T_{1} = tr;2. Compute the average infiltration rate along the border by averaging the rates as both ends at time T_{1}:
_{} (96)3. Compute the 'relative' water surface slope:
_{} (97)4. Compute a revised estimate of the depletion time, T_{2}:
_{} (98)5. Compare T_{2} with T_{1} to determine if they are within about one minute, then the depletion time td is determined. If the analysis has not converged then let T_{1} = T_{2} and repeat steps 2 through 5.
The computation of depletion time given above is based on the algebraic analysis reported by Strelkoff (1977).
vii. Compare the depletion time with the required intake opportunity time. Because recession is an important process in border irrigation, it is possible for the applied depth at the end of the field to be greater than at the inlet. If t_{d} > r_{req}, the irrigation at the field inlet is adequate and the application efficiency, E_{a} can be calculated with Eq. 69 using the following estimate of time of cutoff:
t_{co} = t_{d}  y_{o} L / (2 Q_{o}) (99)If t_{d} < r_{req}, the irrigation is not complete and the cutoff time must be increased so the intake at the inlet is equal to the required depth. The computation proceeds as follows:
t_{co} = r_{req}  y_{o} L / (2 Q_{o})(100)and then E_{a} is computed with Eq. 69.
Since the application efficiency will vary with Q_{o} several designs should be developed using different values of inflow to identify the design discharge that maximizes E_{a}.
viii. Finally, the border width, W_{o} in m is computed and the number of borders, N_{b}, is found as:
W_{o} = Q_{T}/Q_{o} (101)and,
N_{b} = W_{t}/W_{o} (102)where W_{t} is the width of the field. Adjust W_{o} until N_{b} is an even number. If this width is unsatisfactory for other reasons, modify the unit width inflow or plan to adjust the system discharge, Q_{T}.
The computations needed to evaluate and design blockedend borders where the flow is cut off before or shortly after the advance phase is complete are substantially more detailed than the procedures outlined above for furrow and openend border irrigation systems. In fact, the volume balance methods given previously are relatively weak for this particular case of surface irrigation. Generally, the computations for blockedend borders are best performed with zeroinertia or full hydrodynamic simulation models which are beyond the scope of this paper.
A number of studies have been made to develop relationships among the most important variables involving border irrigation using a dimensionless approach and the higher level simulation models. The interested reader might want to refer to Strelkoff and Katapodes (1977), Strelkoff and Shatanawi (1984), Shatanawi and Strelkoff (1984), and Yitayew and Fangmeier (1984) for some of these reports.
The design procedure outlined below is an extension of the approaches already given and consistent with the level of treatment given herein. The procedure given here is intended to be conservative and will yield designs capable of performing at somewhat lower application efficiencies than is perhaps possible using the more comprehensive methods.
The suggested design steps are as follows:
i. Determine the input data as for furrow and border systems already discussed.ii. Compute the maximum inflows per unit width using Eq. 67 with p_{1} = 1.0 and p_{2} = 1.67. The minimum inflows per unit width can also be computed using Eq. 93.
iii. Compute the require intake opportunity time, r_{req}.
iv. Compute the advance time for a range of inflow rates between Q_{max} and Q_{min}, develop a graph of inflow, Q_{o} verses the advance time, t_{L}, and extrapolate the flow that produces an advance time equal to r_{req}. Define the time of cut off, t_{co}, equal to r_{req}. Extrapolate also the r and p values in Eq. 32 found as part of the advance calculations.
v. Calculate the depletion time, t_{d}, in min, as follows:
t_{d} = t_{co} + y_{o} L / (2 Q_{o}) = r_{req} + y_{o} L / (2 Q_{o}) (103)vi. Assume that at t_{d}, the water on the surface of the field will have drained from the upper reaches of the border to a wedgeshaped pond at the downstream end of the border and in front of the dyke.
vii. At the end of the drainage period, a pond should extend a distance l metre upstream of the dyked end of the border. The value of l is computed from a simple volume balance at the time of recession:
_{} (104)where,
Z_{o} = k t_{da} + f_{o} t_{d} (105)and:
Z_{L} = k (t_{d}  t_{L})^{a} + f_{o} (t_{d}  t_{L}) (106)If the value of l is zero or negative, a downstream pond will not form since the infiltration rate is high enough to absorb what would have been the surface storage at the end of the recession phase. In this case the design can be derived from the openended border design procedure. If the value of l is greater than the field length, L, then the pond extends over the entire border and the design can be handled according to the basin design procedure outlined in a following section.
The depth of water at the end of the border, y_{L}, will be:
y_{L} = l S_{o} (107)viii. The application efficiency, E_{a}, can be computed using Eq. 56. However, the depth of infiltration at the end of the field and at the distance Ll metres from the inlet should be checked as Eq. 56 assumes that all areas of the field receive at least Z_{req}. The depths of infiltrated water at the three critical points on the field, the head, the downstream end, and the location l can be determined as follows for the time when the pond is just formed at the lower end of the border:
Z_{1} = k (t_{d}  t_{L}_{1})^{a} + f_{o} (t_{d}  t_{L}_{1}) (108)where,
t_{L}_{1} = [(Ll) / p]^{1/}^{a} (109)It should be noted again by way of reminder that one of the fundamental assumptions of the design process is that the root zone requirement, Z_{req}, will be met over the entire length of the field. If, therefore, in computing E_{a}, one finds Z_{L}_{1} or Z_{L} less than Z_{req}, then either the time of cutoff should be extended or the value of Z_{req} used should be reduced. Likewise, if the depths applied at l and L significantly exceed Z_{req}, then the inflow should be terminated before the flow reaches the end of the border. If the inflow is cut off before the advance phase is completed, the analysis above will have to be replaced by the judgement and experience of the designer, or the more advanced models will have to be utilized.
The problem. In subsection 5.4.4, an example of furrow design was given in which the soil was quite heavy (low infiltration rates). To generate a basis for what might be an interesting comparison of borders and furrow systems, suppose the original question for that field is extended to whether or not borders might be as good. Let us assume that the infiltration characteristics are the same except adjusted for an increased wetted perimeter.
The approximate wetted perimeter for the furrows is found by returning to the flow area, perimeter, and depth relationships. At a flow of 0.09 m^{3}/min, the flow area found in the furrow example was (Eq. 48):
_{}
From Eq. 40 from which the furrow shape was extracted:
y = (154 cm^{2} / 3.331)^{1/1.732} = 9.15 cm
From Eq. 41:
WP = 5.922 * 9.5^{.805} = 35.18 cm.
Since the furrows were spaced at .5 m intervals, one could approximate the infiltration of a border by adjusting the k and f_{o} values by a factor of 1.4 based on the ratio of border to furrow wetted perimeter (50/35.18). If the furrows were operated in the 100 m direction where the slope is .8 percent, the multiplication factor would be about 2.0. For this exercise, the 1.4 factor will be utilized. Thus,
First Irrigation Conditions:Z = 0.00484 t ^{.388} + 0.00008 tLater Irrigation Conditions:
Z = 0.0053 t ^{.327} + 0.000052 t
The units of Z are again m^{3}/m of length/unit width. One would not expect the border infiltration equation to more than double furrow infiltration with furrows spaced less than 1 m apart. Again Mannings n can be 0.04 for initial irrigations and .1 for later irrigations due to crop cover. Z_{req} is 8 cm.
Basic calculations. Assuming also that the soil is relatively stable, Eq. 67 is used to calculate the maximum inflow per unit width for the first irrigation along the 200 m length where erosion is most likely:
_{}
And similarly for irrigations along the 100 m (SO = 0.008) direction:
_{}
The minimum flow suggested by Eq. 93 using later field roughness where spreading may be a problem is for the 200 m lengths:
Q_{min} = 0.000357 * 200 * .001^{.5} / .10 = 0.0226 m^{3}/min/m
or in the 100 m direction:
Q_{min} = .000357 * 100 * .008^{.5} / .10 = 0.032 m^{3}/min/m
The required intake opportunity times found according to the procedure suggested by Eq. 59 are:
First Irrigations r_{req} = 388.5 minLater Irrigations r_{req} = 678.9 min
The next basic calculation, as with furrows, must be to formulate the relationship between advance time and inflow discharge. Starting with a flow near the maximum and working downward using the processes already outlined, advance curves for both infiltration conditions and flow directions can be found. The results for this example are shown in Figure 59.
Figure 59. Dischargeadvance relationship for the border example problem
The last of the basic calculations concerns the depletion and recession times for various values of flow. One illustration should demonstrate this procedure adequately. For an inflow of 0.06 m^{3}/min/m, the advance time along the 200 m length under later conditions is about 145 min. From Eq. 48:
_{}
The time of recession at the lower end of the field, t_{r}, is determined as:
tr = r_{req} + t_{L} = 679 + 145 = 824 min
The time of depletion must be iteratively determined from Eqs. 96  98:
a. t_{d} = t_{r} = 824 minb. _{}
c. _{}
d. _{}
e. Since T_{1} is not close to T_{2}, steps b  d must be repeated with T_{1} set equal to 677 min:
b. _{}
c. _{}
d. _{}
e. Again another estimate of t_{d} seems to be required by the difference found between the iterations. If steps b  d are repeated, the new value of T_{2} is 680 min and the procedure has converged.
The time of cutoff, t_{co}, is found from Eq. 99:
t_{co} = t_{d}  A_{o} L / (2 Q_{o}) = 680  .0355 * 200 / .12 = 631 min.
Finally the application efficiencies of the alternative flows and flow directions are found using Eq. 56. An example for the 0.072 m^{3}/min/m flow along the 200 m direction during the later irrigations is:
_{}
This series of computations is repeated for the full range of discharges, field lengths and infiltration conditions. The following table gives a detailed summary of selected options for the first and subsequent irrigation conditions running in both the 200 m and 100 m directions.
First Irrigations L = 200 m
Sets 
Border Width 
Unit Flow 
Advance Time 
Cutoff Time 
Recession Time 
Field OnTime 
Application Efficiency Percent 
m 
m^{3}/min 
hrs 
hrs 
hrs 
hrs 

2 
50 
0.036 
6.36 
11.34 
12.83 
22.67 
65.3 
3 
33 
0.0545 
3.11 
8.10 
9.59 
24.29 
60.4 
4 
25 
0.072 
2.14 
7.12 
8.61 
28.49 
52.0 
5 
20 
0.09 
1.64 
6.63 
8.12 
33.16 
44.7 
Later Irrigations L = 200 m
Sets 
Border Width 
Unit Flow 
Advance Time 
Cutoff Time 
Recession Time 
Field OnTime 
Application Efficiency Percent 
m 
m^{3}/min 
hrs 
hrs 
hrs 
hrs 

1 
100 
0.018 
15.55 
23.66 
26.86 
23.66 
62.6 
2 
50 
0.036 
5.03 
13.12 
16.34 
26.24 
56.5 
3 
33 
0.0545 
3.15 
11.25 
14.47 
33.76 
43.4 
First Irrigations L = 100 m
Sets 
Border Width 
Unit Flow 
Advance Time 
Cutoff Time 
Recession Time 
Field OnTime 
Application Efficiency Percent 
m 
m^{3}/min 
hrs 
hrs 
hrs 
hrs 

2 
100 
0.018 
5.27 
11.21 
11.74 
22.42 
66.1 
3 
67 
0.0269 
2.35 
8.30 
8.83 
24.89 
59.8 
4 
50 
0.036 
1.44 
7.39 
7.92 
29.55 
50.1 
5 
40 
0.045 
1.03 
6.98 
7.51 
34.91 
42.4 
Later Irrigations L = 100 m
Sets 
Border Width 
Unit Flow 
Advance Time 
Cutoff Time 
Recession Time 
Field OnTime 
Application Efficiency Percent 
m 
m^{3}/min 
hrs 
hrs 
hrs 
hrs 

1 
200 
0.009 
12.89 
23.07 
24.20 
23.07 
64.2 
2 
100 
0.018 
3.45 
13.61 
14.76 
27.23 
54.4 
Field layout and configuration. The field water supply, Q_{T}, established in the furrow example was 1.8 m^{3}/min which would have a duration of 48 hours. Usually, border irrigation would require a higher discharge than furrow systems, but as a first attempt at the problem, consider the field supply fixed.
The options for field layout are to align the borders in either the 200 m or the 100 m directions. The alternative configurations outlined by the data in the preceding tables indicate that there is probably not a strong advantage in irrigating in either direction and the decision can be based on other practical factors. For instance, dividing the field into two, 50 m wide borders running along the 200 m length may be preferable if farming operations are mechanized. During later irrigations, both borders would be irrigated simultaneously with the water supply. The potential application efficiency of this border design would be 6365 percent which is better than furrow systems without cutback or reuse but not as good as the cutback or reuse options.
The problem. Section 5.5.4 illustrated the openend border design procedure. The option of dyking these borders should be considered as an option for improving application efficiency. From results already available, the required intake opportunity times, r_{req}, needed to apply a depth of 8 cm (Z_{req}) were about 389 minutes and 679 minutes for initial and subsequent field conditions, respectively. Assuming the borders will run in the 200 m direction on the 0.1 percent slope as above, Figure 59 indicates the inflows that will complete the advance in the respective r_{req} times are 0.036 m^{3}/min/m for initial irrigations and 0.0215 m^{3}/min/m for later ones.
The values of r and p need to be generated or extrapolated for these flow rates unless they are already generated as part of the development of Figure 59 or, in this example case, from the previous example problem. For the 0.036 m^{3}/min/m inflow, the values of r and p were determined from the previous example as r =.5635 and p = 6.949. For the 0.0215 m^{3}/min/m inflow, r and p were calculated using the methods outlined in section 5.3.1 rather than extrapolated with the result that r =.6032 and p = 3.916.
All other inputs to this problem like infiltration coefficients and roughness are assumed to be the same as in section 5.5.3.
To this point, the blockedend border design procedure outlined in section 5.5.2 is completed through step iv. The remainder of the steps are as follows:
v. Calculate the depletion time, t_{d}, in min, as follows:t_{co} = r_{req} = 389 min_{} (94)
t_{d} = t_{co} + y_{o} L / (2 Q_{o}) = 389 + .0134 * 200 / (2 * .036) = 426 min (103)
vi. Assume that at 426 min the water on the surface of the field has drained into the wedgeshaped pond at the downstream end of the border.
vii. At 426 min, a pond should extend a distance of l metre upstream of the dyked end of the border. The value of l is:
Z_{o} = k t_{da} + f_{o} t_{d} = .00484 * 426^{.388} + .00008 * 426 = 0.0848 m^{3}/m/m (105)Z_{L} = k (t_{d}  t_{L})^{a} + f_{o} (t_{d}  t_{L}) = .00484 * (426  389)^{.388} + .00008 * (426  389) = 0.0226 m^{3}/m/m (106)
_{} (104)
_{}Since the value of l is between zero and L a downstream pond will form and infiltrate in place to fill the root zone. The depth of water at the end of the border, y_{L}, will be:
y_{L} = l S_{o} = 80.8 * .001 = 0.0808 m (105)viii. The application efficiency, E_{a}, can be computed using Eq. 56. However before making this computation, it is instructive to compute the depths of infiltration along the border. The application at the inlet was found above to be 0.0848 m or about 8.5 cm. At the end of the border, the application is Z_{L} from above plus y_{L}, or .1034 m. The depth of infiltration at the distance L1 metres from the inlet is:
t_{L}_{1} = [(L  1) / p]^{1/}^{r} = (119.2 / 6.949)^{1/.5635} = 155 minZ_{1} = k (t_{d}  t_{L}_{1})^{a} + f_{o} (td t_{L}_{1}) (107)
= .00484 * (426  155)^{.388} + .00008 * (426  155) = 0.064 mAs one immediately determines, the middle of the field is underirrigated. If fact, if E_{a} is calculated from Eq. 56,
_{} (56)one sees that the results are distorted. The assumption that the entire field receives the required depth, Z_{req}, is implicit in Eq. 56. It cannot be used unless this condition is met. And since the objective of the design is to completely refill the root zone, either the time of cutoff needs to be extended or the design value of Z_{req} should be reduced to approximate the depth infiltrated in the least watered areas to ensure this constraint. The simplest option is to adjust Z_{req} to say 0.06 m and utilize the values of inflow and cutoff time developed above. If this is decided upon, the application efficiency according to Eq. 56 is 85.7% which is a substantial improvement over the openend design. The other option is to extend the cutoff time so the ponded wedge extends further up the basin. This involves several repetitions of the design procedure given above in a trial and error search for the cutoff time that works. Given the precarious nature of the volume balance procedure for the blockedend border case in the first place, this later option is not recommended. If a better design is sought, the more advanced simulation models will have to be used.
Now other field configurations must be tested and compared. The eventual selection will be the one with the best performance over both infiltration conditions. These calculations will be left to the interested reader. One note should be made at this point however. The computer program given at the end of this paper does not include an option or blockedend borders.
Basin irrigation design is somewhat simpler than either furrow or border design. Tailwater is prevented from exiting the field and the slopes are usually very small or zero. Recession and depletion are accomplished at nearly the same time and nearly uniform over the entire basin. However, because slopes are small or zero, the driving force on the flow is solely the hydraulic slope of the water surface, and the uniformity of the field surface topography is critically important.
An effort will not be made to develop a design procedure for irregularly shaped basins or where the advancing front is very irregular. Rather, the water movement over the basin is assumed to occur in a single direction like that in furrows and borders. Three further assumptions will be made specifically for basin irrigation. First, the friction slope during the advance phase of the flow can be approximated by:
S_{f} = y_{o} / x (110)
in which y_{o} is the depth of flow at the basin inlet in m, x is the distance from inlet to the advancing front in m, and S_{f} is the friction slope. Utilizing the result of Eq. 112 in the Manning equation yields:
_{}
or,
_{} (112)
The second assumption is that immediately upon cessation of inflow, the water surface assumes a horizontal orientation and infiltrates vertically. In other words, the infiltrated depth at the inlet to the basin is equal to the infiltration during advance, plus the average depth of water on the soil surface at the time the water completes the advance phase, plus the average depth added to the basin following completion of advance. At the downstream end of the basin the application is assumed to equal the average depth on the surface at the time advance is completed plus the average depth added from this time until the time of cutoff.
The third assumption is that the depth to be applied at the downstream end of the basin is equal to Z_{req}. Under these three basic assumptions, the time of cutoff for basin irrigation systems is (assume y_{o} is evaluated with x equal to L):
_{} (113)
The time of cutoff must be greater than or equal to the advance time.
Basin design is much simpler than that for furrows or borders. Because there is no tailwater problem, the maximum unit inflow also maximizes application efficiency.
Thus, the design procedure does not need to search among various flow rates for a value that meets a design criterion like finding the deep percolationfield tailwater tradeoff point. Basin dimensions therefore become more a matter of practicality to the farmer than one of hydraulic necessity.
As a guide to basin design, the following steps are outlined:
i. Input data common to both furrows and borders must first be collected. Field slope will not be necessary because basins are usually 'dead level'.ii. The required intake opportunity time, r_{req}, can be found as demonstrated in the previous examples.
iii. The maximum unit flow should be calculated along with the associated depth near the basin inlet. The maximum depth can be approximated by Eq. 112:
_{} (114)and then perhaps increased 1020 percent to allow some room for postadvance basin filling. If the computed value of y_{max} is greater than the height of the basic perimeter dykes, then Q_{max} needs to be reduced accordingly. The maximum unit flow, Q_{max}, is difficult to assess. During the initial part of the advance phase, flow velocities will be greater than later in the advance. As a general guideline, it is suggested that Q_{max} be based on the flow velocity in the basin when the advance phase is oneninth completed. The basin equivalent to Eq. 67 is:
_{} (115)Usually the design of basins will involve flows much smaller than indicated in Eq. 115.
iv. Select several field layouts that would appear to yield a well organized field system and for each determine the length and width of the basins. Then compute the unit flow, Q_{o} for each configuration as:
Q_{o} = Q_{T} / W_{b} (116)where W_{b} is the basin width in m. As noted above, the maximum efficiency will generally occur when Q_{o} is near Q_{max} so the configurations selected at this phase of the design should yield inflows accordingly.
v. Compute the advance times, t_{L}, for each field layout as discussed in subsection 5.3.1, the cutoff time, t_{co}, from Eq. 113 (if t_{co} < t_{L}, set t_{co} = t_{L}), and the application efficiency using Eq. 56. The layout that achieves the highest efficiency while maintaining a convenient configuration for the irrigator/farmer should be selected.
The problem. A comparison of basin irrigation with the furrow and border systems in previous subsections should provide an interesting view of the three systems collectively. To remind the reader, an irrigation project is in the planning stages in which a basic field block of 2 hectares has been chosen for field design. A preliminary survey has revealed that the fields are configured in 100 m widths and 200 m lengths. The typical slopes are .8% in the 100 m dimension and .1% in the other. Soils appear to be relatively nonerosive and have been tested to yield the following infiltration functions:
First Irrigations Z = 0.00484 r ^{.388} + 0.00008 rLater Irrigations Z = 0.0053 r ^{.327} + 0.000052 r
Z has units of m^{3}/m of length/m of width, and r has units of minutes. Anticipated application depths per irrigation based on an evaluation of cropping patterns and crop water requirements are 8 cm.
The water supply to the field is set by the project at 1.8 m^{3}/min, available for 36 hours every 10 days. Quality of water supply is good and hopefully these deliveries will be made as expected so far as rate, duration, and frequency are concerned.
For the purposes of design, the Manning roughness coefficient for first irrigations will be taken as 0.04 and for the later irrigations as 0.10. This is to reflect a bare soil condition for first irrigations and a cropped surface for later irrigations.
Basic calculations. The intake opportunity times for the two field conditions are the same as found earlier for borders, namely:
r_{req} = 389 min for initial irrigations
and,
r_{req} = 679 min for later irrigations
Maximum flows permissible assuming a 30 cm perimeter dyke around the basins and flows running in the 100 m direction are found from Eq. 115:
_{}
Utilizing Figures 53af, the advance time as a function of unit flow can be determined as indicated below. The Q_{o} verses t_{L} data are plotted in Figure 60.
Figure 60. Dischargeadvance relationships for the basin example
Q_{O} 
_{} 
_{} 
_{} 
_{} 
_{} 
First Irrigations  
0.40 
0.0649 
1.00 
0.020 
0.022 
17.8 
0.20 
0.0471 
1.22 
0.040 
0.050 
29.4 
0.10 
0.0342 
1.48 
0.080 
0.120 
57.3 
0.05 
0.0248 
1.81 
0.160 
0.300 
93.0 
0.03 
0.0196 
2.09 
0.267 
0.750 
183.8 
Later Irrigations  
0.40 
0.099 
0.62 
0.013 
* 
* 
0.20 
0.072 
0.78 
0.026 
0.030 
41.5 
0.10 
0.052 
0.98 
0.052 
0.061 
61.0 
0.05 
0.038 
1.20 
0.104 
0.155 
113.3 
0.03 
0.030 
1.41 
0.173 
0.430 
248.1 
Field layout. Basins installed on sloping fields should have their longest dimension running normal to the largest field slope in order to minimize land levelling costs. Thus, for this example where the basins have been selected with a 100 m length, they would have their direction of flow parallel to the 200 m direction. The width is a choice left to the designer. Some of the options, their dimensions and performance are summarized below. Figure 61 shows a 10 basin configuration.
No. of Basins 
Basin Width 
Unit Flow 
Advance Time 
Cutoff Time 
Field Irrig. Time 
Application Efficiency 
m 
m^{3}/min 
min 
min 
hrs 
% 

First Irrigations 

4 
50 
0.036 
140 
316 
21.1 
70.3 
6 
33 
0.054 
90 
201 
20.1 
73.7 
8 
25 
0.072 
68 
147 
19.6 
75.6 
10 
20 
0.09 
55 
116 
19.3 
76.6 
12 
17 
0.108 
45 
94 
18.8 
78.8 
20 
10 
0.18 
31 
56 
18.7 
79.4 
Later Irrigations 

4 
50 
0.036 
175 
327 
21.8 
68.0 
6 
33 
0.054 
105 
197 
19.7 
75.2 
8 
25 
0.072 
80 
143 
19.1 
77.7 
10 
20 
0.09 
68 
114 
19.0 
78.0 
12 
17 
0.108 
60 
95 
19.0 
78.0 
20 
10 
0.18 
43 
58 
19.3 
76.6 
Figure 61. Example basin configuration
One of the advantages of basins that immediately becomes apparent is that field division is much more flexible. Application efficiencies can be very high and nearly all options are workable in terms of the water supply.
It is not possible to illustrate effectively the judgement or 'art' required to evaluate and design surface irrigation systems. The previous examples demonstrate the procedures described in this guide and, to a limited extent, alert the reader to factors he or she will need to determine on a case by case basis. There are major influences on the design process one might expect which lie far outside a mathematical treatment. For example, the size and shape of individual land holdings and their future change in response to customs for inheritance, governmental interventions such as land consolidation and resettlement, farmer preference and attitudes, harvesting and cultivating equipment limitations, etc. In short, there is not a universal algorithm for design and evaluation that eliminates the need for good judgement. On the other hand, good judgement is no substitute for the mathematical aids presented herein. One might demonstrate this by comparing the performance of a system properly designed with one where selection of inflow and cutoff time is made arbitrarily.
To be skilled in design is to completely understand the relationships among the selectable and manageable variables governing surface irrigation, particularly the effects of infiltration and stream size on advance. The mathematical treatment, if followed, helps illustrate some of the more important individual processes occurring in the field.
Because the irrigator has the latitude of changing flow rates and cutoff times, the field system may not respond as designed. The problem is unlike sprinkler and trickle irrigation where having selected and installed the system's piping, the hydraulics of the system's operation are defined. Consequently, surface irrigation design cannot provide a guaranteed level of performance but must rely on the farmer to operate and manage it efficiently. It is apparent therefore, that the role of extension and technical assistance to farmers is critical for surface irrigated regimes.
As a final thought in this section, something should be stated regarding costs associated with surface irrigation. It would be most desirable to present a comprehensive review, but such is impractical because surface irrigation systems themselves are so widely varied. Table 9 lists a number of irrigation technologies and a figure representing the costs. The units here are $/ha but should be used only to indicate the relative magnitude of various system costs under agricultural conditions typical of the western United States. Other systems enter the picture as one moves from country to country.
Table 9 TOTAL ANNUAL COSTS FOR SELECTED ONFARM IRRIGATION SYSTEMS
Description of System or Improvement 
Annual Costs, $/ha 
Concrete ditch linings 
40 
Gatedpipe 
35 
Cutback systems 
100 
Reuse systems with gatedpipe 
150 
Solidset sprinklers 
500700 ^{1} 
Hand  moved sprinklers 
300450 
Wheelline or sideroll sprinklers 
200300 
Centrepivot sprinklers 
150200 
Trickle irrigation 
5001000 
^{1} The pressurized systems are often supplied by groundwater wells onfarm. The range of costs is for surface supplies (small values) and for groundwater (larger values).