water pressure on the inner surface of a cylinder 1

[maisir666]

i have been trying to find a formula or any equations which can calculate or any theories which states on finding the stress values and displacements of points on the cylinder wall by point water pressures using nozzle sprays.
the water pressure is about 20MPa n the cylinder is about 5mm thick with a inner diameter of 90mm.i want to find a way to get stress values or dsplacement values in the point where the water spray pressure is applied. it would be great if i can get a solution for this as soon as possible.

 

[mtnengr]

You can separate the problem into two parts. From your aero background, you should be able to calculate the stagnation pressure (ps) of the fluid stream at the cylinder. Assume a flat plate for a start. You need to establish the effective radius of the stream at the wall as a function of distance of the nozzle from the wall. Then, you need to determine the response of stresses and displacements.

Assume a single cosine half wave pressure distribution using the effective radius previously assumed with an amplitude ps.

Calculate the effective pressure distrubution for the cylinder by expanding the applied cosine pressure into a Fourier series for the entire circumference of the cylinder.

Now you have an even function of pressure fourier harmonics to determine the stresses and displacements on the cylinder. These values are dictated upon the where the stream is applied on the cylinder and the boundary conditions of the cylinder.

There are several FEM applications that can give you the answers you need.

Good luck

 

[EricZhao]

For quick hand calculation, assume there isn't pressure loss from the nozzle and to the wall. The net pressure on the cylinder wall would be P = 20MPa. Since the wall thickness t = 5mm << r = 90mm. The wall could be considered as thin wall shell.

The problem is close to pure shear stress status.

3.14*R^2*P = t*2*3.14*R*\sigma

=>

\sigma = R*P/(2*t) = (R / 10) * 20MPa

where R is the radium of the water jet in millimeter.

 

[EricZhao]

I assumed the radium of the water jet is small compared with 90mm

 

[mtnengr]

To EricZhao:

The formula pr/2t is for an applied axisymmetric pressure. If the pressure is in a localized region, the resulting stresses are much more than just membrane. The resonse is local bending, membrane and shear stresses. You can not claim a state of shear as the predominat state.

The true solution for a pressure being applied to a cyliderical cap is given by Ernest Paxon in a Stanford PHd thesis, approximately 1970. The equations are very, very complex.