Question Bank • QB_PARAMETRIC_SWCE_DYN_004 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Dynamics of Flow & Bernoulli Equation

Subtopic: Venturimeter pressure differential

Question Statement:

Water flows through a horizontal pipe of diameter $20\text{ cm}$ tapering to $10\text{ cm}$ at a rate of $0.090\text{ m}^3/\text{s}$. Neglecting frictional losses, the pressure drop between the inlet and throat is ________ $\text{kPa}$ (round off to two decimal places). (Variation QB_PARAMETRIC_SWCE_DYN_004)

Answer Key:

61.55

Step-by-Step Solution & Explanation

From continuity: $A_1 = \frac{\pi}{4} (0.20)^2 = 0.03142\text{ m}^2 \implies v_1 = \frac{0.09}{A_1} = 2.865\text{ m/s}$ $A_2 = \frac{\pi}{4} (0.10)^2 = 0.00785\text{ m}^2 \implies v_2 = \frac{0.09}{A_2} = 11.459\text{ m/s}$ Applying Bernoulli's equation for horizontal pipe ($z_1 = z_2$): $P_1 - P_2 = \frac{1}{2} \rho (v_2^2 - v_1^2) = \frac{1000}{2} (11.459^2 - 2.865^2) = 61550.0\text{ Pa} = 61.55\text{ kPa}$
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