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What is the rate of flow in a rectangular channel 4 m wide and 2 m deep with a bed slope of 1 in 900 when it running full if Chezy’s constant is 50?

Given,

width (B) = 4 m

depth (y) = 2 m

Bed slope S0 = 1/9000

Chezy’s constant (C) = 50

Area of flow (B × y) = 4 × 2 = 8 m2

Perimeter (R) = (B + 2y) = 4 + 2 × 2 = 8 m

Hydraulic radius, R = A/p = 8/8 = 1 m

Discharge, \(Q = AC\sqrt {R{S_o}}\)

= $$ \(\begin{array}{l} 8 \times 50 \times \sqrt {1 \times \frac{1}{{900}}} \\ \\ 8 \times 50 \times \frac{1}{{30}} \end{array}\)

=13.33 m3/s