Hello! In the attached JPG, I boxed in an area where I'm working through the integration of an engineering differential equation. Here are the terms in the problem:
z = axis along the centerline of the pipe
p = pressure, which is a function of z
r = radius of a pipe (varies from centerline to R)
vz = velocity, which is a function of r
mu = constant value (i.e., viscosity)
R = constant value (i.e., outer radius)
Near the top of the boxed area of the attachment, I show the start of the integration. I have to integrate twice with respect to r, to get the answer listed at the bottom of the page. I can't seem to get the right answer and I believe the last term might be causing my trouble (i.e., the term noted as needing integration by parts).
Basically, I need to know how to solve this partial differential equation to its analytical solution, but I'm not sure what I'm doing wrong.
Thanks in advance,
M Ridzon
z = axis along the centerline of the pipe
p = pressure, which is a function of z
r = radius of a pipe (varies from centerline to R)
vz = velocity, which is a function of r
mu = constant value (i.e., viscosity)
R = constant value (i.e., outer radius)
Near the top of the boxed area of the attachment, I show the start of the integration. I have to integrate twice with respect to r, to get the answer listed at the bottom of the page. I can't seem to get the right answer and I believe the last term might be causing my trouble (i.e., the term noted as needing integration by parts).
Basically, I need to know how to solve this partial differential equation to its analytical solution, but I'm not sure what I'm doing wrong.
Thanks in advance,
M Ridzon
