Question

A horizontal Venturimeter with inlet diameter of 30 cm and throat diameter of 15 cm is used to measure the flow of water. The reading on a differential manometer connected to the inlet and the throat is 20 cm of mercury. If C_d = 0.98, the rate of flow is nearly
1. 12.5 l/s
2. 25 l/s
3. 125 l/s
4. 250 l/s

Answer 1

Correct Answer - Option 3 : 125 l/s

Concept:

The rate of flow from Venturimeter is given as

\(Q = \;{C_d}\frac{{{A_1}{A_2}}}{{\sqrt {A_1^2 - A_2^2} }} \times \sqrt {2gh} \)

Where,

A₁ and A₂ are cross sectional area at inlet and throat section

h = differential manometer head

\(h = X\;\left( {\;\frac{{{\rho _{Hg}}}}{\rho } - 1} \right)\)

Where,

X = differential manometer reading

Calculation:

Given,

d₁ = 30 cm ; d₂ = 15 cm, C_d = 0.98, x = 20 cm

\({A_1} = \frac{\pi }{4}{\left( {0.3} \right)^2} = 0.07065\;{m^2}\)

\({A_2} = \frac{\pi }{4}{\left( {.15} \right)^2} = .01766\;{m^2}\)

\(h = 0.2 \times \left( {\frac{{13.6}}{1} - 1} \right) = 2.52\;m\)

\(Q = 0.98 \times \frac{{.07065\; \times .\;01766}}{{\sqrt {{{\left( {.07065} \right)}^2} - {{\left( {01766} \right)}^2}} }} \times \sqrt {2 \times 9.81 \times 2.52} \)

Q = 128 l/s

Q ≈ 125 l/s