Question Bank • QB_SUB_SWCE_0091 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Continuity equation, kinematics and dynamics of flow

Question Statement:

Water flows through a horizontal pipe reducing from diameter $d_1 = 20\text{ cm}$ to $d_2 = 10\text{ cm}$. If the velocity at section 1 is $v_1 = 1.5\text{ m/s}$, the velocity at section 2 ($v_2$, in m/s) by continuity equation is:

Answer Key:

6.0

Step-by-Step Solution & Explanation

Continuity equation for incompressible fluid: $A_1 v_1 = A_2 v_2 \implies v_2 = v_1 \left(\frac{d_1}{d_2}\right)^2 = 1.5 \times \left(\frac{0.2}{0.1}\right)^2 = 1.5 \times (2)^2 = 6.00\text{ m/s}$
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