Question Bank • QB_SWCE_EXP_003 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Continuity equation, kinematics and dynamics of flow

Question Statement:

A horizontal pipe of diameter $200\text{ mm}$ abruptly enlarges to a diameter of $400\text{ mm}$. If water flows through the pipe at a rate of $0.0628\text{ m}^3\text{/s}$, the head loss due to sudden expansion in meters of water is ________ (round off to 3 decimal places). Take $g = 9.81\text{ m/s}^2$.

Answer Key:

0.115

Step-by-Step Solution & Explanation

1. Cross-sectional areas: $A_1 = \frac{\pi}{4} (0.20)^2 = 0.031416\text{ m}^2$ $A_2 = \frac{\pi}{4} (0.40)^2 = 0.125664\text{ m}^2$ 2. Flow velocities: $V_1 = \frac{Q}{A_1} = \frac{0.0628}{0.031416} = 2.0\text{ m/s}$ $V_2 = \frac{Q}{A_2} = \frac{0.0628}{0.125664} = 0.50\text{ m/s}$ 3. Borda-Carnot head loss equation for sudden expansion: $h_e = \frac{(V_1 - V_2)^2}{2 g} = \frac{(2.0 - 0.50)^2}{2 \times 9.81} = \frac{1.50^2}{19.62} = \frac{2.25}{19.62} \approx 0.11468\text{ m} \approx 0.115\text{ m}$
← Previous (QB_SWCE_ADV_100) Next (QB_SWCE_FM_003) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test