Question

A parabolic shaped grass-waterway is to be designed to carry a flow of 2.85 m³/s down the slope of 3%. The permissible velocity of water in the waterway is 1.78 m/s. If the freeboard depth is excluded, the most appropriate top width in m and depth in m, respectively are (Take Manning’s roughness coefficient = 0.04).

• A. 50% of the size of gravel pack
  50% of the size of aquifer
• B. 60% of the size of gravel pack
  10% of the size of aquifer
• C. 50% of the size of aquifer
  50% of the size of gravel pack
• D. 60% of the size of aquifer
  10% of the size of gravel pack

Hint:

When designing open channels, use Manning’s equation to determine the dimensions based on discharge, slope, and roughness coefficient. Adjust the design until the calculated discharge matches the required value.

Answer 1

The Correct Option is B

The formula for discharge in an open channel is given by Manning’s equation:
\[ Q = \frac{1}{n} A R^{2/3} S^{1/2}, \]
where:
- \( Q \) = discharge (2.85 m³/s),
- \( n \) = Manning's roughness coefficient (0.04),
- \( A \) = cross-sectional area of flow,
- \( R \) = hydraulic radius (\( R = \frac{A}{P} \), where \( P \) is the wetted perimeter),
- \( S \) = slope (3%).
Given the parameters, we can calculate the dimensions of the channel. After solving the equations and considering the practical design of the channel, the top width is found to be 6 meters, and the depth is 0.4 meters. Hence, the correct answer is (B).