## Q. 5.3

A venturimeter is fitted in a horizontal pipe to measure the discharge. The inlet diameter and the throat diameter are 40 cm and 20 cm respectively. The reading in the differential manometer with mercury is 8 cm. Determine the discharge if the coefficient of venturimeter is 0.98.

## Verified Solution

Area $A_{1}=\frac{\pi }{4}×(0.4 )^{2}$

= 0.1256 m²

Area $A_{2}=\frac{\pi }{4}×(0.2 )^{2}$

= 0.031415 m²

The difference of pressure head in manometer is

$h=x(\frac{s_{m} }{s_{p} }-1 )$

$=0.08(\frac{13.6}{1}-1 )$=1 m of water

Now, using the discharge equation of venturimeter,

$Q=C_{d}\frac{A_{1}A_{2} }{\sqrt{A^{2}_{1}-A^{2}_{2} } }\sqrt{2gh}$

Substituting values in Eq. (i), we have

$Q=0.98\frac{0.1256 \times 0.31415}{\sqrt{0.12562^{2} – 0.031415^{2} } }\sqrt{2×9.81×1}$

Q =1.409 m³/s