Answer to Question #183596 in Vector Calculus for aman

Question

An oil of sp.gr.0.8 is flowing through a Venturimeter having inlet diameter 20 cm and throat diameter 10 cm. The oil-mercury differential manometer shows a reading of 25 cm. Calculate the discharge of oil through the horizontal Venturimeter. Take Cd = 0.98.

Answer 1

Given sp.gr of oil $s_0 = 0.8$

sp.gr of mercury $s_h = 13.6$

Reading of differential manometer = 25cm

We have that,

Difference of pressure head $h = x[\frac{s_h}{s_0}-1] = 25[\frac{13.6}{0.8}-1] = 400 cm$ of oil

Diameter of inlet $(d_1) = 20cm$

$a_1 = \frac{\pi d^2_1}{4} = \frac{400\pi}{4} = 314.16 cm^2$

Diameter of throat $(d_2) = 10cm$

$a_2 = \frac{\pi d^2_2}{4} = \frac{100\pi}{4} = 78.54 cm^2$

$c_d = 0.98$

The discharge Q of the oil is gotten using

$Q =c_d \dfrac{a_1a_2}{\sqrt{a_1^2 - a_2^2}}\sqrt{2gh}$

$Q =0.98 \dfrac{314.16×78.54}{\sqrt{314.16^2 - 78.54^2}}\sqrt{2×9.8×400}$

$Q \approx 7,038 cm^3s^{-1} = 7.038 lts^{-1}$