Irrigation System Designing - Practices of Irrigation and On-farm Water Management - page 83

term in both Eqs. ( 3.7 ) and ( 3.8 ) relates to the temporal acceleration term, and the
following two terms stem from the advective accelerations in x and y- directions;
these account for the inertia effects.
Based on these shallow water flow equations, numerous models have been
developed for basin irrigation design. But the solution approaches of the govern-
ing equations differ from each other. The two-dimensional hydrodynamic model
has been extended to incorporate micro-topography (Playan et al., 1996 ) , irreg-
ular boundaries (Singh and Bhallamudi, 1997 ) , non-level basin (Bradford and
Katopodes, 2001 ) , and many other particular situations.

3.3.3.2 Zero-Inertia Model

Probably Strelkoff et al. ( 1996 , 2003 ) were the first to attempt to develop a
simulation model for basin irrigation in two-dimensions using the zero-inertia
approximation. The developed model simulates two-dimensional flow from a point
or line source in an irrigated basin with a non-level soil surface. The govern-
ing equations used were obtained by simplifying the full hydrodynamic from of
the equations (Eqs . 3.6 , 3.7 and 3.8 ) by neglecting the inertial terms. The effect
of the inertial terms becomes small compared with those describing the effect of
depth gradient gravity and friction in shallow water flow. This is typical of agri-
cultural fields where the flow process is more diffusional in nature due to the low
velocities.
The continuity equation can be obtained by expressing q x =

uh and q y = vh, dis-

charge per unit width (m 2 /s) in the x - and y -directions, respectively. Using

∂ h /∂ t =

∂ H /∂ t and substituting q x and q y in Eq. ( 3.6 ) yields

x + ∂

∂ H

∂ t + ∂

q x
∂

q y
∂

y +

I s = 0 (3.9)

By neglecting the inertial terms in Eqs. ( 3.2 ) and ( 3.3 ) become

∂ H

∂ x +

S fx = 0 (3.10)

∂ H

∂

y +

S fy = 0 (3.11)

3.3.3.3 Other Approaches

Clemmens and Strelkoff ( 1979 ) developed dimensionless advance curves, using
the zero-inertia approach for level basin irrigation design. Khanna et al. ( 2003b ,
c ) developed a two-dimensional model for the design of rectangular basin, and
irregular shape and multiple basins. In both the cases, the model's governing equa-
tions are based on a zero-inertia approximation to the two-dimensional shallow