Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2022
Medium
A steady two-dimensional flow field is specified by the stream function ψ=kx³y, where x and y are in meter and the constant k=1 m⁻²s⁻¹. The magnitude of acceleration at a point (x,y)=(1 m, 1 m) is ___________ m/s² (round off to 2 decimal places).
4.24 m/s²(± 0.05 accepted)
Explanation
u=∂ψ/∂y=kx³, v=−∂ψ/∂x=−3kx²y. At (1,1): u=1, v=−3. ax=u(∂u/∂x)+v(∂u/∂y)=1(3kx²)+(−3)(0)=3. ay=u(∂v/∂x)+v(∂v/∂y)=1(−6kxy)+(−3)(−3kx²)=1(−6)+(−3)(−3)=−6+9=3. |a|=√(3²+3²)=√18≈4.24.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.