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GATE ME 2016 Set 3 — Question 51

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MCQ+2 / -0.67MediumLocal, Convective & Material AccelerationFluid Kinematics & DynamicsFluid MechanicsContinuity & Momentum Equations

Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations

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Question

For a two-dimensional flow, the velocity field is u⃗=xx2+y2i^+yx2+y2j^\vec{u} = \frac{x}{x^2 + y^2} \hat{i} + \frac{y}{x^2 + y^2} \hat{j}, where i^\hat{i} and j^\hat{j} are the basis vectors in the x−yx-y Cartesian coordinate system. Identify the CORRECT statements from below.
(1) The flow is incompressible.
(2) The flow is unsteady.
(3) y-component of acceleration, ay=−y(x2+y2)2a_y = \frac{-y}{(x^2 + y^2)^2}
(4) x-component of acceleration, ax=−(x+y)(x2+y2)2a_x = \frac{-(x + y)}{(x^2 + y^2)^2}
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