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A channel designed using Lacey’s theory has mean velocity of 1m/sec and silt factor of one, the hydraulic radius for channel will be:-
1. 2 m
2. 2.5 m
3. 1.0 m
4. 0.50 m

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Correct Answer - Option 2 : 2.5 m

Concepts:

The basic and derived equation for Lacey’s theory is:

Basic Equations

Derived Equations

\(V^2 = \frac{2}{5} fR ; f = 1.76 \sqrt{D_{50}}\)

\(V = {(\frac{Qf^2}{140})}^{1/6}\)

\(Af^2 = 140 V^5\)

P = 4.75 √Q

\(V = 10.8 R^{2/3} S^{1/3}\)

 \(R = 0.48 {[\frac{Q}{f}]}^{1/3}\)

Where

f = silt factor; R = Hydraulic radius, Q = discharge, P = wetted Perimeter; V= velocity of flow; S= slope

Calculations:

Given: V = 1m/s; f = 1;

Using the equation: \(V^2 = \frac{2}{5} fR ; f = 1.76 \sqrt{D_{50}}\)

\((1)^2 = \frac{2}{5} \times 1 \times R\)

We get

R = 2.5 m

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