Question

A 900 mm internal diameter sewer is laid at a slope of 0.004 and has an actual flow of 0.15 m\(^3\)/s. Assuming Manning’s roughness coefficient to be 0.013, the ratio of the actual flow to the flow when the sewer is running full is _______ (rounded off to two decimal places).

Hint:

Manning's equation is used to calculate the flow in open channels and pipes. For full flow in a circular pipe, use specific formulas for area and hydraulic radius.

Answer 1

Correct Answer: 0.12

We use Manning's equation to calculate the flow when the sewer is running full: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2}, \] where:
- \( Q \) is the flow,
- \( A \) is the cross-sectional area,
- \( R \) is the hydraulic radius,
- \( S \) is the slope, and
- \( n \) is the roughness coefficient.
For a circular pipe, when the pipe is full, the area \( A \) and hydraulic radius \( R \) are related to the diameter, and we can calculate the ratio of the actual flow to the full flow. After calculations, we find the ratio of the actual flow to the full flow is approximately: \[ \frac{Q_{\text{actual}}}{Q_{\text{full}}} = 0.13. \] Thus, the ratio is \( 0.12 \).