Question

find the velocity potential when a sphere in moving with constant velocity in a liquid which in otherwise at rest​

Answer 1

Answer:

A sphere of radius a moves with constant velocity U in a fluid otherwise at rest. How far ahead of the sphere is there a disturbance of magnitude 1/20.U? Show that the acceleration of a fluid particle at distance x ahead of the centre of the sphere is

3U2(a3x4−a6x7)

I think I've got that the potential function is

−Ua32r2cosθ

but i'm not sure how to go further to answer the question.

Answer 2

Answer:

• In a fluid that is otherwise at rest, a sphere of radius travels with constant velocity U. A disturbance of magnitude 1/20.
• U is located how far in front of the sphere?
• Demonstrate that a fluid particle moving forward of the sphere's center at a distance x accelerates at 3U2(a3x4−a6x7)
• I believe I understand what the potential use is Ua32r2cosθ

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