Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2021
Hard
A two dimensional flow has velocities in x and y directions given by u = 2xyt and v = −y²t, where t denotes time. The equation for streamline passing through x=1, y=1 is
- Ax²y = 1
- xy² = 1
- Cx²y² = 1
- Dx/y² = 1
Explanation
dy/dx = v/u = −y²t/(2xyt) = −y/(2x). Separating: dy/y = −dx/(2x) ⟹ ln y = −(1/2)ln x + C ⟹ y·x^(1/2) = K. At x=1,y=1: K=1, so y²x=1, i.e. xy²=1.
Source: GATE ME 2021 Session 2 (ME-2) (2021)
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