Q) A 30 cm diameter sewer having an invert slope of 1.200 was flowing hill. What would be velocity of flow and discharge ?(n=0.013). Is the velocity self cleaning? What would be the velocity and discharge when the same is flowing 0.2 and 0.8 of its full depth?

Given:

$n=0.013$

$d=30cm$

$s=\frac{1}{200}$

To find:

1. Velocity self cleansing:-

$Q=\frac{1}{n}AR^\frac{2}{3}s\frac{1}{2}=\frac{1}{0.013}*(\frac{π }{4}*(0.3)^2)*(\frac{1}{200})^\frac{1}{2}$

$=76.92*(0.071)*0.176*0.071=0.067cumsec $

Velocity=$\frac{Q}{A}=\frac{0.067}{\frac{π }{4}*(0.3)^2}=\frac{0.067}{0.071}=0.94m/sec$

$assume \frac{q}{Q}=0.333$

From given table:-

$\frac{v}{V}=0.898$

$v=0.898*v$

$=0.898*0.94$

$=0.844m/sec \gt 0.45 m/sec$

This is greater than self cleansing of 0.45m/sec

2. Velocity and discharge when the flawing with 0.2 and 0.8 of its full length:-

for, $\frac{d}{D}=0.2$

$\frac{V}{v}=0.615$

$V=0.615*0.94=0.5781m/sec=0.58m/sec$

similarly, for $\frac{d}{D}=0.2$

$\frac{q}{Q}=0.088$

$q=0.088*0.067$

$q=0.0059 cumecs$

$\frac{d}{D}=0.8$

$\frac{v}{V}=1.140$

$V=1.140*0.94$

$=1.0716m/sec$

$V=1.072m/sec$

$\frac{q}{Q}=0.9781$

$q=0.9781*0.067$

$q=0.066 cumecs$