Question

The pressure drop through a well-designed constriction is to be used for measuring the velocity of flow through a circular pipe. If the pressure drop from a 0.1 m diameter section to a 0.05 m diameter section of the pipe is 7.5 kPa, the velocity in m/s in the 0.1 m diameter section of the pipe is __________. (Take density of liquid = 1000 kg/m³)

• A. 0.5
• B. 1.0
• C. 1.5
• D. 2.0

Hint:

When calculating velocity from pressure drop in pipe constrictions, use Bernoulli’s equation and the continuity equation to relate pressure difference and velocities.

Answer 1

The Correct Option is B

The velocity of flow can be calculated using the principle of conservation of energy and Bernoulli’s equation. For the two sections of the pipe, we use the equation:
\[ \Delta P = \frac{\rho (v_2^2 - v_1^2)}{2}, \]
where:
- \( \Delta P \) = pressure difference (7.5 kPa),
- \( \rho \) = density of the liquid (1000 kg/m³),
- \( v_1 \) = velocity in the 0.1 m diameter section,
- \( v_2 \) = velocity in the 0.05 m diameter section.
By using the continuity equation:
\[ A_1 v_1 = A_2 v_2, \]
where \( A_1 = \frac{\pi d_1^2}{4} \) and \( A_2 = \frac{\pi d_2^2}{4} \), and solving the equations, we find that the velocity in the 0.1 m diameter section is 1.0 m/s. Hence, the correct answer is (B).