Fluid pressure close to an accelerating plate

[chocolativore]

Hi all,

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

 

[Chestermiller]

The fluid in the tube is being accelerated at the same rate as the pipe. So artificial gravity is being created within the fluid. This would be described by the hydrostatic equation: $$\frac{dp}{dz}=-\rho a$$where a is the acceleration and z is the distance from the capped end. So, at distance z, $$p=p_c-\rho a z$$where $p_c$ is the pressure at the capped end.