Question Bank • QB_SWCE_FM_003
MCQ • 1 Mark
Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Continuity equation, kinematics and dynamics of flow
Question Statement:
A two-dimensional velocity field is given by $\vec{V} = (4x)\hat{i} - (4y)\hat{j}$. This flow field represents:
Options:
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(A) Incompressible and irrotational flow
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(B) Incompressible and rotational flow
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(C) Compressible and irrotational flow
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(D) Compressible and rotational flow
Step-by-Step Solution & Explanation
1. Incompressibility check via 2D continuity equation:
$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = \frac{\partial}{\partial x}(4x) + \frac{\partial}{\partial y}(-4y) = 4 - 4 = 0$
Since the divergence is zero, the flow is incompressible.
2. Irrotationality check via vorticity $\omega_z$:
$\omega_z = \frac{1}{2} \left( \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \right) = \frac{1}{2} (0 - 0) = 0$
Since vorticity is zero, the flow is irrotational. Thus, Option A is correct.
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