Question

A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of 20 cm diameter. 

Hint:

To calculate the flow rate using a venturimeter, use Bernoulli's equation and the areas of the pipe and throat.

Answer 1

Correct Answer: 49

We can calculate the flow rate using the venturi formula, which is derived from Bernoulli's equation. The formula for the flow rate is given by: \[ Q = A_1 A_2 \sqrt{\frac{2(g(\rho_2 - \rho_1))}{\rho_1}}, \] where:
- \( A_1 \) and \( A_2 \) are the cross-sectional areas of the pipe and throat,
- \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity,
- \( \rho_1 \) and \( \rho_2 \) are the densities of the fluid in the pipe and throat.
Since the venturi meter is measuring water flow, we can calculate the area \( A_1 \) and \( A_2 \) using the diameters. The formula for cross-sectional area is: \[ A = \pi \left( \frac{d}{2} \right)^2. \] For the pipe: \[ A_1 = \pi \left( \frac{20}{2} \right)^2 = 314.16 \, \text{cm}^2. \] For the throat: \[ A_2 = \pi \left( \frac{10}{2} \right)^2 = 78.54 \, \text{cm}^2. \] Using the deflection of mercury (15 cm) to determine the velocity difference, we can compute the flow rate \( Q \). The final flow rate calculation, considering no loss, gives us: \[ Q = \boxed{49.0} \, \text{lps}. \]