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Question

In a flow field the stream lines and equipotential lines

A
Are parallel
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B
Cut at any angle
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C
Are orthogonal every where in the field
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D
Cut orthogonal expect at the stagnation points
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Solution

The correct option is D Cut orthogonal expect at the stagnation points
For equi-potential line:
dϕ=0
udxvdy=0
dydx=uv
Hence, slope of equipotential line,
(dydx)ϕ=constant=uv.....(i)
For equi-stream function line:
dΨ=0
vdx-udy=0 [stream line]
dxu=dyv
and dydx=vu
Hence slope of equi-stream line,
(dydx)Ψ=constant=vu....(ii)
From equation (i)and (ii)
(dydx)ϕ=constant×(dydx)Ψ=constant
=uv×vu=1
Hence, stream lines and equipotential lines are orthogonal to each other expect at the stagnation points.

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