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Two-Dimensional And Axisymmetric Motion

PYQs

Two-Dimensional And Axisymmetric Motion

1) In an axisymmetric motion, show that stream function exists due to equation of continuity. Express the velocity components of the stream function. Find the equation satisfied by the stream function if the flow is irrotational.

[2015, 20M]

Consider the motion of fluid in cylindrical coordinates. The equation of continuity is given by:

For incompressible fluid and steady flow,

For axi-symmetric flow,

Now the condition that may be an exact differential. Let it be equal to .

and
and
which satisfy continuity equation. Also, the streamlines are given by:

exists due to equation of continuity.

If flow is irrotational, then (potential) exists, such that

,
Also,
,
Also,

2) Consider a uniform flow in the positive . A cylinder of radius is located at the origin. Find the stream function and the velocity potential. Find also the stagnation points.

[2015, 10M]

2015-5(d)

Complex potential, at

Since ,

and

At stagnation point, ,

and and , ,

3) Show that the velocity distribution in axial flow of viscous incompressible fluid along a pipe of annular cross-section radii , is given by .

[2001, 30M]

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