Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2017
Hard
For a steady flow, the velocity field is V = (-x² + 3y)î + (2xy)ĵ. The magnitude of the acceleration of a particle at (1,-1) is
- A2
- B1
- 2√5
- D0
Explanation
aₓ = u∂u/∂x + v∂u/∂y = (-x²+3y)(-2x) + (2xy)(3) = 2x³-6xy+6xy = 2x³. At (1,-1): aₓ=2. a_y = u∂v/∂x + v∂v/∂y = (-x²+3y)(2y) + (2xy)(2x) = -2x²y+6y²+4x²y = 2x²y+6y². At (1,-1): a_y = -2+6=4. |a| = √(2²+4²) = √20 = 2√5.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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