Question

The maximum quantity of water expected in one the longitudinal drains on clayey soil is 0.9 cum/s. If the Manning's roughness coefficient is 0.02 and allowable velocity of flow is 1.2 m/s, then the cross sectional area (in sq. m) would be
1. 0.02
2. 0.75
3. 45.00
4. 1.33
5. 0.03

Answer 1

Correct Answer - Option 2 : 0.75

Concept:

The relation between discharge (Q), velocity of flow (V) and area of cross section (A) is given as:

 Q = A × V

Calculation:

Given: 

Maximum permissible discharge, Q = 0.9 m³/sec.

Allowable velocity of flow, V = 1.2 m/s

Q = A × V

Or

0.9 = A × 1.2

∴ Area of cross section required, A = 0.75 m².

Note:

As per Manning’s formula, the velocity of flow is given as:

\(V = \frac{1}{N}\;{R^{2/3}}{S^{1/2}}\)

Where,

N is the roughness coefficient

S is the bed slope

R is hydraulic depth which is the ratio of wetted area to wetted perimeter.