Allied & ICAR Exam Bank • ALLIED_2687 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

The volumetric flux of an incompressible velocity field $\vec{v}$ through a closed surface $S$ enclosing volume $V$ is:

Options:

  • (A) $0$
  • (B) $V$
  • (C) $\int_V |\vec{v}| dV$
  • (D) $\infty$

Answer Key:

A

Step-by-Step Solution & Explanation

By Gauss's divergence theorem, flux is $\iint_S \vec{v} \cdot d\vec{S} = \iiint_V (\nabla \cdot \vec{v}) dV$. Since the fluid is incompressible, $\nabla \cdot \vec{v} = 0$, so net flux is zero.
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