GATE ME 2015 Set 2 — Question 22
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Fluid Mechanics → Fluid Kinematics & Dynamics → Streamlines, Pathlines & Streaklines
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Question
If the fluid velocity for a potential flow is given by with usual notations, then the slope of the potential line at is
Correct answer
(B) -(u)/(v)
Solution
For a potential flow, a velocity potential exists such that the velocity components are and .
A potential line (equipotential line) is defined by .
Taking the total differential: .
Substituting the velocity components: .
Rearranging for the slope: .
Thus, the slope of the potential line is .
A potential line (equipotential line) is defined by .
Taking the total differential: .
Substituting the velocity components: .
Rearranging for the slope: .
Thus, the slope of the potential line is .
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