SSC JE Civil Engineering 23 Mar 2021 Shift 1 Paper

Concepts: The flow in sewer pipe takes place under atmospheric conditions i.e. open channel flow and also its is assumed to be a uniform flow. Hence, Manning’s formula can be applied for the calculation of discharge, which is given as : $Q=A\left(\frac{1}{N} R^{2/3} S^{1/2}\right)$ Where N is roughness coefficient, depends on pipe material R hydraulic radius depends on pipe geometry S is bed slope at which pipe is laid A is a cross-sectional area Q is the rate of flow in sewer pipe Calculation: Since, both sewer pipelines have same diameter and made of same material, they have same hydraulic radius and cross section area and roughness coefficient. Therefore, it can be concluded that $Q \alpha S^{1/2}$ Now , $\frac{Q_{A}}{Q_{B}} = \frac{S_{A}^{1/2}}{S_{B}^{1/2}}$ $\frac{Q_{A}}{Q_{B}} = \frac{\left(\frac{1}{225}\right)^{1/2}}{\left(\frac{1}{625}\right) \frac{1}{2}}$ $\frac{Q_{A}}{Q_{B}} = 1.67$