water pressure on the inner surface of a cylinder
water pressure on the inner surface of a cylinder
(OP)
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.
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.





RE: water pressure on the inner surface of a cylinder
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
RE: water pressure on the inner surface of a cylinder
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.
RE: water pressure on the inner surface of a cylinder
I assumed the radium of the water jet is small compared with 90mm
RE: water pressure on the inner surface of a cylinder
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.