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 :
$\mathrm{Q}=\mathrm{A}\left(\frac{1}{\mathrm{N}}{\mathrm{R}}^{2∕3}{\mathrm{S}}^{1∕2}\right)$
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
$\mathrm{Q}\mathrm{\alpha }{\mathit{S}}^{1∕2}$
Now ,
$\frac{{\mathrm{Q}}_{\mathrm{A}}}{{\mathrm{Q}}_{\mathrm{B}}}=\frac{{\mathrm{S}}_{\mathrm{A}}^{1∕2}}{{\mathrm{S}}_{\mathrm{B}}^{1∕2}}$
$\frac{{\mathrm{Q}}_{\mathrm{A}}}{{\mathrm{Q}}_{\mathrm{B}}}=\frac{{\left(1∕225\right)}^{1∕2}}{\left(1∕625\right)1∕2}$
$\frac{{\mathrm{Q}}_{\mathrm{A}}}{{\mathrm{Q}}_{\mathrm{B}}}=1.67$