## Q. 4.1

A pipe having diameter 30 cm at a section carries oil of specific gravity 0.8 at a velocity of 2 m/s. At another section, the diameter is 20 cm. Find the velocity at this section and also the mass rate of flow of the oil.

## Verified Solution

Given $D_{1}$ = 30 cm = 0.3 m, $D_{2}$= 20 cm = 0.2 m, Specific gravity of oil s = 0.8 and $V_{1}$= 2 m/s
From continuity Eq. (4.3), we have

$Q=A_{1}V_{1}=A_{2}V_{2}$

Or                                                $\frac{\pi }{4}D^{2}_{1}\times2=\frac{\pi }{4}D^{2}_{2}\times V_{2}$

Or                                                 $V=(\frac{D_{1} }{D_{2} } )^{2}\times2=(\frac{0.3}{0.2} )^{2}\times 2=4.5 m/s$

Mass rate of flow of oil $=\rho _{\omicron }A_{1}V_{1}$

$=0.8\times 1000\times \frac{\pi }{4}\times(0.3)^{2}\times 2=113.097 kg/s$