Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2020
Medium
The velocity field of an incompressible flow in a Cartesian system is represented by V⃗ = 2(x²−y²)î + vĵ + 3k̂. Which one of the following expressions for v is valid?
- A−4xz + 6xy
- −4xy − 4xz
- C4xz − 6xy
- D4xy + 4xz
Explanation
For incompressible flow, ∂u/∂x+∂v/∂y+∂w/∂z=0. Here ∂u/∂x=4x and ∂w/∂z=0, so ∂v/∂y=−4x, giving v=−4xy+g(x,z) for any function g. Only option (B), −4xy−4xz, has the required −4xy term (with g(x,z)=−4xz).
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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