Question

In a venturimeter, the flow is 0.15 m$^3$/s when the differential pressure is 30 kN/m$^2$. What is the flow when the differential pressure is 60 kN/m$^2$?

• A. 0.212 m$^3$/s
• B. 0.106 m$^3$/s
• C. 0.3 m$^3$/s
• D. 0.075 m$^3$/s

Hint:

In venturimeter calculations, remember that flow is proportional to the square root of the pressure ratio, so when pressure doubles, the flow increases by a factor of \(\sqrt{2}\).

Answer 1

The Correct Option is A

For a venturimeter, the flow rate is related to the differential pressure according to the equation: \[ Q_1 = Q_2 \sqrt{\frac{P_1}{P_2}} \] Where:
- \(Q_1\) is the flow rate at differential pressure \(P_1\)
- \(Q_2\) is the flow rate at differential pressure \(P_2\)
- \(P_1\) and \(P_2\) are the differential pressures at two conditions
Given:
- \(Q_1 = 0.15 \, \text{m}^3/\text{s}\), \(P_1 = 30 \, \text{kN/m}^2\)
- \(P_2 = 60 \, \text{kN/m}^2\)
Using the formula: \[ Q_2 = Q_1 \sqrt{\frac{P_2}{P_1}} = 0.15 \times \sqrt{\frac{60}{30}} = 0.15 \times \sqrt{2} = 0.15 \times 1.414 = 0.212 \, \text{m}^3/\text{s} \] Therefore, the flow rate when the differential pressure is 60 kN/m$^2$ is 0.212 m$^3$/s.