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GATE 2019 ME (ME2) – Question 19

Fluid Mechanics · Differential equations of continuity and momentum, velocity potential · 1 mark · Multiple choice

A two-dimensional incompressible frictionless flow has $\vec u=x\hat i-y\hat j$. With fluid density ρ, find its pressure-gradient vector.

  1. $\rho(x\hat i+y\hat j)$
  2. $-\rho(x\hat i+y\hat j)$
  3. $\rho(x\hat i-y\hat j)$
  4. $-\rho(x^2\hat i+y^2\hat j)$

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Correct answer: (B) $-\rho(x\hat i+y\hat j)$

Explanation

Convective acceleration is $(u u_x+v u_y,u v_x+v v_y)=(x,y)$. Euler’s equation gives $\nabla p=-\rho\vec a=-\rho(x\hat i+y\hat j)$. **B**.