GATE ME 2018 Set 1 — Question 44
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Fluid Mechanics → Fluid Kinematics & Dynamics → Local, Convective & Material Acceleration
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Question
In a Lagrangian system, the position of a fluid particle in a flow is described as and where is the time while , , and are constants. The flow is
Correct answer
(B) steady and two-dimensional
Solution
In the Lagrangian description, the position of a particle is given by and .
The velocity components are obtained by differentiating the position with respect to time:
In the Eulerian description, the velocity field is .
The velocity components are obtained by differentiating the position with respect to time:
In the Eulerian description, the velocity field is .
1.Steadiness: Since the velocity components and at any fixed point do not depend on time (i.e., and ), the flow is steady.
2.Dimensionality: Since there are two non-zero velocity components ( and ) that vary with spatial coordinates, the flow is two-dimensional.
Therefore, the flow is steady and two-dimensional.Continue learning with Success Tracker
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