Water Conveyance Loss and Designing Conveyance System - Practices of Irrigation and On-farm Water Management - page 14

1.2.5 Hydraulic Design of Open Irrigation Channel

We always search for an efficient and economic channel section. The most economic
section is one which can carry maximum discharge for a given cross-sectional area,
or, in other words, the channel which requires minimum cross-sectional area (or
excavation) for a given discharge. For practical purposes, discharge is fixed, and the
minimum cross-sectional area is of interest.

1.2.5.1 Condition for Maximum Discharge Through a Channel
of Rectangular Section

The earthen channel of rectangular section is not used except in heavy clay or rocky
soils, where the faces of rocks can stand vertically. A concrete channel of rectangu-
lar configuration is generally used. Thus, the hydraulically efficient section of the
concrete channel is important.
Let us consider a channel of rectangular section as shown in Fig. 1.4 . Let

Fig. 1.4 Sketch of a
rectangular channel section

Freeboard

Flow
Depth, d

Width, b

b = width of the channel and

d depth of flow

Then, area of flow, A

=

= b × d

C √ RS )
where R is the hydraulic radius, and S is the slope of the channel.
We know, hydraulic radius, R

AC √ RS (since V Discharge, Q = A × V = =

A
P .

=

AC P S
Taking S , A , and C constant in the above equation, the discharge will be
maximum when A / P is maximum, or the perimeter P is minimum.
We get wetted perimeter P

Thus, Q =

= b + d + d = b + 2 d (from Fig. 1.4 ) ,

and A = b × d ,or b = A / d

A
d +

Thus, P = 2 d

To find the minimum value of P , we have to differentiate the function, set it equal
to zero, and solve for variable d . That is,