GATE ME 2019 Set 2 — Question 19
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Fluid Mechanics → Fluid Kinematics & Dynamics → Euler & Bernoulli Equations
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Question
A two-dimensional incompressible frictionless flow field is given by . If is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as
Correct answer
(B) -ρ(xi + yj)
Solution
For a steady, incompressible, and frictionless flow, the pressure gradient is related to the acceleration by Euler's equation (neglecting body forces):Given the velocity field , we have and . The convective acceleration components are:Thus, the acceleration vector is . Substituting this into Euler's equation:
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