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I need to calculate the pressure in a fluid at some fixed distance from a flat plate which is accelerating (normal to its surface) through a fluid.

If you assume the plate to be infinite (i.e. a rigid half-space), then I think the problem can be formalised as a one dimensional problem:

Imagine a rigid, semi-infinite, one-dimensional pipe, with one end which is capped. This could be visualised as a test-tube of infinite height. The pipe is filled with an idealised inviscid fluid of density ρ and bulk modulus K. The pipe is subjected to a constant acceleration A, parallel to its length. How can I calculate the pressure in the fluid at a point along the length of the pipe which is a constant distance X from the capped end?

Does anyone have any ideas or experience with this kind of problem?

Thank you in advance

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# Fluid pressure close to an accelerating plate

Can you offer guidance or do you also need help?

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