Correct Answer - Option 2 : 2.5 m
Concepts:
The basic and derived equation for Lacey’s theory is:
Basic Equations
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Derived Equations
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\(V^2 = \frac{2}{5} fR ; f = 1.76 \sqrt{D_{50}}\)
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\(V = {(\frac{Qf^2}{140})}^{1/6}\)
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\(Af^2 = 140 V^5\)
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P = 4.75 √Q
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\(V = 10.8 R^{2/3} S^{1/3}\)
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\(R = 0.48 {[\frac{Q}{f}]}^{1/3}\)
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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