The hydraulic radius of a circular sewer of internal diameter 100 cm, running in fully occupied cross section is given by:

Question

Question

This question was previously asked in

SSC JE Civil 15 Nov 2022 Shift 1 Official Paper

Answer 1

Concept:

The hydraulic mean depth or also called hydraulic radius is defined as:

\(R = \frac{{\rm{Wetted}\;\rm{Area}}}{{\rm{Wetted}\;\rm{perimeter}}}=\frac{A}{P}\)

Wetted area = \(A = \frac{\pi }{4}{d^2} \)

Wetted perimeter P = πd

Hydraulic mean deppth = \(R = \frac{A}{P} = \frac{{\pi {d^2}}}{{4\pi d}} = \frac{d}{4}\)

Calculation

Given:

d = 100 cm.

For circular pipe:

\(R = \frac{A}{P} =\frac{d}{4}\)

\(R =\frac{100}{4}=25\;mm\)