GATE ME 2014 Set 4 — Question 53
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Fluid Mechanics → Fluid Kinematics & Dynamics → Streamlines, Pathlines & Streaklines
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Question
Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii) is the differential equation of a streamline, where , and are velocities in directions , and , respectively
(iv) In an unsteady flow, the path of a particle is a streamlineWhich one of the following combinations of the statements is true?
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii) is the differential equation of a streamline, where , and are velocities in directions , and , respectively
(iv) In an unsteady flow, the path of a particle is a streamlineWhich one of the following combinations of the statements is true?
Correct answer
(D) (i), (ii), (iii)
Solution
Statement (i) is the definition of a streamline. Statement (ii) follows from the definition because the velocity vector is tangent to the streamline, meaning there is no velocity component normal to it. Statement (iii) is the standard differential equation for a streamline derived from . Statement (iv) is false because pathlines and streamlines only coincide in steady flow; in unsteady flow, they are generally different.
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