Question

A venturimeter, having a diameter of 7.5 cm at the throat and 15 cm at the enlarged end, is installed in a horizontal pipeline of 15 cm diameter. The pipe carries an incompressible fluid at a steady rate of 30 litres per second. The difference of pressure head measured in terms of the moving fluid in between the enlarged and the throat of the venturimeter is observed to be 2.45 m. Taking the acceleration due to gravity as 9.81 m/s${}^2$, the coefficient of discharge of the venturimeter (correct up to two places of decimal) is

• A. 0.95

Answer 1

The correct option is A 0.95

$Q=30l/s$
$(\frac{P_1}{w}+Z_1)-(\frac{P_2}{w}+Z_2)=2.45m=h$
$$g=9.81$$
$Q=C_d\frac{A_1{A}_2}{\sqrt{A_1^2-A_2^2}}\sqrt{2gh}$
$C_d=\frac{Q}{\frac{A_1{A}_2}{\sqrt{A_1^2-A_2^2}}\sqrt{2gh}}$
$=\frac{30\times {10}^{-3}{m}^3/s}{\frac{\frac{\pi }{4}{\left(0.15\right)}^2\times {\left(0.075\right)}^2}{\sqrt{{\left(0.15\right)}^2-{\left(0.075\right)}^2}}\times \sqrt{2\times 9.81\times 2.45}}$
C${}_d=0.95$