Design procedure for furrow cutback systems

Any procedure which attempts to maximize application efficiencies will determine the minimal waste trade-off 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 non-cutback 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 c₁ and c₂ are empirical coefficients, h is the head over the outlets, in m, and A is the outlet area in cm2.

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 non-erosive 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:

N₁ = Q_T/Q_o (73) For the second set,

N₂ = (Q_T - N₁Q_cb)/Q_o (74) and similarly,

N_i = (Q_T - N_i-1Q_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 procedure-trying 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 A₂ = - CBR (77)

for k > 2 (78) Then the number of furrows in the first set is:

N₁ = N_f/(k + A) (79)

for k = 2 N₂ = N_f - N₁ or,

for k > 2 N₂ = (1 - CBR)N₁ (80) and,

set first value of B = - CBR (81) N_j = N₁ (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 = N₁Q_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 cross-slope.