Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2023
Hard
The velocity field of a certain two-dimensional flow is given by V(x,y)=k(xî−yĵ), where k=2 s⁻¹ and x,y are in meters. Gravitational effects are negligible. If the density of the fluid is 1000 kg/m³ and the pressure at the origin is 100 kPa, the pressure at the location (2m, 2m) is ______ kPa.
84 kPa(± 1 accepted)
Explanation
u=kx, v=−ky; vorticity=∂v/∂x−∂u/∂y=0, so the flow is irrotational and Bernoulli applies between any two points. At (0,0): speed=0, P0=100kPa. At (2,2): u=4, v=−4, speed²=32. P=P0−(1/2)ρ(V²−V0²)=100000−0.5×1000×32=100000−16000=84000 Pa=84 kPa.
Source: GATE ME 2023 Official Paper (2023)
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