For a discharge of 100 cumec to flow at a depth 5.0 m in a rectangular horizontal channel, the width as per Lacey's theory should be

Question

Question

This question was previously asked in

BPSC AE Paper 6 (Civil) 14 Oct 2022 Official Paper

Answer 1

Concept

As per Lacey’s formula, the relation between discharge, Q, and the wetted perimeter is given as:

\(P = 4.75\;\sqrt Q \)

For a rectangular channel, wetted perimeter P is given as:

P = B + 2 × y

Where y is the depth of flow.

If the channel is very wide the P ≈ B (as y ≪ B)

Calculation:

Given: Q = 100 cumecs; y = 5 m, B =?

Now,

\(P = 4.75 \times \sqrt {100} = 47.5\;m\)

Further,

P = B + 2 × y

47.5 = B + 2 × 5

⇒ B = 37.5 m