Question

Determine the velocity potential of the (2-D) flow due to a moving circular cylinder with velocity U in the positive x-direction by means of the method of separation of variables. Take the radius of the cylinder as “a” and compare your analytical result with the result obtained by using singularities. 

          Determine the velocity potential of the (2-D) flow due to a moving circular cylinder with velocity U in the positive x-direction by means of the method of separation of variables. Take the radius of the cylinder as “a” and compare your analytical result with the result obtained by using singularities.
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Determine the velocity potential of the (2-D) flow due to a moving circular cylinder with velocity U in the positive x-direction by means of the method of separation of variables. Take the radius of the cylinder as “a” and compare your analytical result with the result obtained by using singularities.
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Transcript

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00:01 So, in order to find the dependence of flow velocity we would require that del square is equal to 1 over r del del r of r del del r.
00:13 So, del p here is negative c so c plus mu del square u r equals 0.
00:21 So, del square u r is equal to minus c over mu.
00:26 So, when we further deduce this, this can be written as this implies d over d r r d u r over d r is equal to minus c r over mu r d u r over d r equals minus c r square over 2 mu plus a.
00:57 So, d u r over d r equals minus c r over 2 mu plus a over r.
01:05 Now, on integrating we would get on integrating we would get that u r is equal to minus c r square over 4 mu plus a log r naught plus b mark this as equation number 1...
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