Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2019
Hard
A two-dimensional incompressible frictionless flow field is given by u⃗=xî−yĵ. If ρ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
- Aρ(xî+yĵ)
- −ρ(xî+yĵ)
- Cρ(xî−yĵ)
- D−ρ(x²î+y²ĵ)
Explanation
For inviscid flow, Euler's equation gives ∇p=−ρa⃗, where a⃗ is the material acceleration. a_x=u∂u/∂x+v∂u/∂y=x(1)+(−y)(0)=x. a_y=u∂v/∂x+v∂v/∂y=x(0)+(−y)(−1)=y. So a⃗=(x,y), and ∇p=−ρ(xî+yĵ).
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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