If a stream is carrying a discharge of 4.0 cumec per meter width having a silt factor 2.0, then the Lacey's scour depth will be

Question

Question

This question was previously asked in

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

Answer 1

Concept:

Lacey's scour depth is given by:

\(R\; = \;1.35{\left( {\frac{{{q^2}}}{f}} \right)^{\frac{1}{3}}}\; \)

Where, q = Discharge per meter width, f = silt factor

Calculations:

Given, q = 4 cumec, f = 2

\(R\; = \;1.35{\left( {\frac{{{4^2}}}{2}} \right)^{\frac{1}{3}}}\;=\;2.14\;m\)

Hence, the most appropriate answer is option 2.

Important Points

Various formulas deduced by lacey is given below:

1) silt factor ⇒ \(\rm{f = 1.76\sqrt {{d_{mm}}}}\)

2) velocity of flow ⇒\(V = {\left[ {\frac{{Q{f^2}}}{{140}}} \right]^{\frac{1}{6}}}\)

3) hydraulic mean depth ⇒\(R = \frac{{5{V^2}}}{{2f}}\)

4) wetted perimeter ⇒ \(P = 4.75\sqrt Q \)