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Given data : Rate of discharge, Q = 550 litres / sec. = 0.55 mÂ³ / sec Bed slope, i = 1 in 2600 = 1 / 2600 Chezyâ€™s constant , C = 60 We know that, the conditions for the most economical rectangular channel are ; â€¢ width, b = 2 Ã— depth = 2d â€¢ Hydraulic mean depth = m = A / P = d / 2 ( where A = area oRead more

Given data :

Rate of discharge, Q = 550 litres / sec. = 0.55 mÂ³ / sec

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

Chezyâ€™s constant , C = 60

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

â€¢ width, b = 2 Ã— depth = 2d

â€¢ 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 . âˆš mi

0.55 = b Ã— d Ã— 60 Ã— âˆš d/2 Ã— 1/2600

9.167 Ã— 10^-3 = 2 Ã— dÂ² Ã— âˆš d/ 2 Ã— 0.0196

0.467 = 2.dÂ² Ã— âˆšd/2

therefore, d = 0.64 m

and b = 2 Ã— d = 1.28 m

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

b = 1.28 mandd = 0.64 m