Laminar flow fixed parallel plates

1. Mar 9, 2013

2. Mar 9, 2013

Staff: Mentor

This all goes back to eqns. 122 and 123, and how you go about solving partial differential equations like these for the pressure. Eqn. 123 can be integrated with respect to y to show that the pressure will be equal to ρgy plus a function of x, f(x) (analogous to the constant of integration in solving an ordinary differential equation). You then substitute that result into equation 122, and find that f(x) is equal to x times the partial derivative of p with respect to x, plus a constant.

3. Mar 9, 2013

MotoPayton

Ok, I get it now. I didn't see the step of bringing that equation back into the PDE's. I was also confused on how the dp/dx was treated as constant wrt x but on the following page it shows that dp/dx is in fact constant and related to the viscosity and spatial properties.
Thank you.