Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2022
Medium
The velocity field in a fluid is given to be V⃗ = (4xy)î + 2(x²−y²)ĵ. Which of the following statement(s) is/are correct?
- AThe velocity field is one-dimensional.
- The flow is incompressible.
- The flow is irrotational.
- The acceleration experienced by a fluid particle is zero at (x=0, y=0).
Explanation
u=4xy, v=2(x²−y²). (A) FALSE: the field depends on both x and y and has two nonzero components — not 1-D. (B) TRUE: ∇·V = ∂u/∂x+∂v/∂y = 4y+(−4y) = 0. (C) TRUE: vorticity ωz = ∂v/∂x−∂u/∂y = 4x−4x = 0. (D) TRUE: acceleration components ax=u∂u/∂x+v∂u/∂y and ay=u∂v/∂x+v∂v/∂y both contain u and v as multiplicative factors; at (0,0), u=v=0, so both ax and ay vanish regardless of the derivative terms.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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