A rectangular channel carries water at the rate of 550 litres/sec when bed slope is 1 in 2600 Find the most economical dimensions of the channel if c=60

Given data :

Rate of discharge, Q = 550 litres / sec. = 0.55 m³ / sec

Bed slope, i = 1 in 2600 = 1 / 2600

Chezy’s constant , C = 60

We know that, the conditions for the most economical rectangular channel are ;

• width, b = 2 × depth = 2d

• Hydraulic mean depth = m = A / P = d / 2

( where A = area of section and P = wet perimeter of section )

Also we know , Q = A . C . √ mi

0.55 = b × d × 60 × √ d/2 × 1/2600

9.167 × 10^-3 = 2 × d² × √ d/ 2 × 0.0196

0.467 = 2.d² × √d/2

therefore, d = 0.64 m

and b = 2 × d = 1.28 m

Hence, the most economical dimension for the given channel are :

b = 1.28 m and d = 0.64 m