The most economical section of a rectangular channel for maximum discharge is obtained when its depth is equal to half the breadth. Most economical rectangular section • Let consider a rectangular channel as shown in figure in which width of channel is b and depth of flow is h. Cross - sectional area of flow = A = bh Wetted Perimeter = P = b + 2h = A/h + 2h
• For most economical section, perimeter should be minimum, i.e.,
dP
dh
=0
dP
dh
=
d
dh
(b+2h)=
d
dh
(
A
h
+2h)=0 −
A
h2
+2=0⇒A=2h2 bh=2h2 b=2h‌or‌h=
b
2
Hence for most economical rectangular section, width is twice the depth of channel.