Chemegate
Home/Practice Tests/PYQ Archive/Fluid Mechanics

GATE 2026 Chemical Engineering, Q37 · Fluid Mechanics

The correct answer is C, The flow is compressible and rotational..

Question

Consider a flow with the following velocity field: V = (x + y) î + (y + z) ĵ + (z + x) k̂, where î, ĵ and k̂ are the unit vectors in the x, y and z directions, respectively. Which one of the following is CORRECT?

  • A. The flow is incompressible and irrotational.
  • B. The flow is incompressible and rotational.
  • C. The flow is compressible and rotational.
  • D. The flow is compressible and irrotational.

Official answer: The flow is compressible and rotational.

Why

GATE 2026 official key: (C). Incompressible requires ∇⋅V=0\nabla \cdot V=0 and irrotational requires ∇×V=0.\nabla \times V=0. Here ∇⋅V=∂(x+y)/∂x+∂(y+z)/∂y+∂(z+x)/∂z=1+1+1=3\nabla \cdot V = \partial (x+y)/\partial x + \partial (y+z)/\partial y + \partial (z+x)/\partial z = 1+1+1 = 3 ≠ 0 (compressible), and ∇×V=(−1,−1,−1)\nabla \times V = (−1,−1,−1) ≠ 0 (rotational).

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

Fluid Mechanics Topic Guide →More Fluid Mechanics PYQs →Take the Full GATE 2026 Test →