Question

Find the volume flow rate in the venturi meter given below in which water is flowing.

• A. 1
• B. \( \sqrt{3} \)
• C. \( 2\sqrt{3} \)
• D. \( \sqrt{2} \)

Hint:

In Bernoulli’s equation, the total energy is conserved, which relates velocity and pressure at different points in a flow.

Answer 1

The Correct Option is A

Step 1: Use Bernoulli’s equation for the venturi meter.
The equation for Bernoulli’s principle is given by: \[ P_A + \frac{1}{2} \rho v_A^2 = P_B + \frac{1}{2} \rho v_B^2 \] Where: \( P_A \) and \( P_B \) are the pressures at points A and B, \( v_A \) and \( v_B \) are the velocities at points A and B, and \( \rho \) is the density of water.
Step 2: Rearranging Bernoulli’s equation.
We can simplify the equation to: \[ P_A - P_B = \frac{1}{2} \rho (v_B^2 - v_A^2) \] This gives the difference in velocity between points A and B.
Step 3: Solve for velocity at A and B.
From the equation: \[ v_B^2 - v_A^2 = 1 \] and \[ A_A v_A = A_B v_B \] Using \( A_A = 2A_B \), we get: \[ 3v_A^2 = 1 \quad \Rightarrow \quad v_A = \frac{1}{\sqrt{3}} \] Step 4: Conclusion.
The flow rate is 1, corresponding to option (1).