Irrigation System Designing - Practices of Irrigation and On-farm Water Management - page 93

and their temporal and spatial variation affect infiltration. Other factors such as ini-
tial soil moisture, cracks and other voids in the soil, soil layering, and heterogeneity,
and water quality, including chemistry and temperature also influence infiltration.
Furrow irrigation performance depends on a number of variables, namely, inflow
rate, cutoff time, furrow length, spacing and shape, roughness, slope, infiltration
characteristics, and irrigation requirement. Variables such as furrow length and slope
are constrained by the field shape and size, infiltration characteristics and roughness
by soil type, and furrow shape and size by equipment. The irrigation requirements
are driven by climate, soil, and crop conditions. All these factors need to be con-
sidered in the decision-making process, but they are generally given, not decision
variables. Thus, for a given set of field and crop conditions, furrow inflow rate and
cutoff time are the decision variables.

3.4.7.2 Simulation of Furrow Design Variables

Simulation Alternatives

Furrow irrigation has been simulated under different considerations. Wu and Liang
( 1970 ) optimized furrow run length using the minimum cost criterion, whereas,
Reddy and Clyma ( 1981 ) optimized furrow irrigation system design without con-
sidering the irrigation schedule or the minimum discharge to assure the advance of
water to the end of the run. Holzapfel et al. (1986, 1987) used linear and nonlinear
optimization models to design surface irrigation systems, considering homoge-
neous soils and regression-derived relationships between irrigation performance and
design variables. Raghuwanshi and Wallender ( 1998 ) used kinematic-wave model
to optimize furrow irrigation.

Kinematic-Wave Model

A kinematic-wave model can be used to represent unsteady and spatially varied
flow in a sloping and free draining furrow. The model consists of the continuity and
a simplified form of the hydrodynamic equation in that friction force is balanced by
furrow bottom slope. Inertial and water depth gradient terms are negligible:

∂

t + ∂

Q
∂ x + ∂

Z
∂

A
∂ r =

0 (3.17)

S r = S 0 (3.18)

the cross-sectional flow area in m 2 , Q the flow rate in m 3 /min, Z where A = = =

infiltration per unit furrow length in m 3 /m, x

= distance in the direction of flow in

m, t = elapsed time in min, T = intake opportunity time in min, S r = friction slope,

and S 0 = furrow bottom slope. Infiltration per unit furrow length ( Z ) can be com-

puted using Eqs. ( 3.19 ) and ( 3.20 ) , which empirically accounts for differences in
infiltration rate along the wetted perimeter section (Bautista and Wallender, 1992 ) :