# Solving an equation with boundary conditions

1. Jul 28, 2009

Hey all,

I finally figured out how to solve the integral:

$$\int{dp} = \int{6U\eta(\frac{h-\overline{h}}{h^{3}})}{dx} + C$$

using maple and have it export to matlab where:

$$h=R+h0-\sqrt{R+x}\sqrt{R-x}$$
$$\overline{h}=R+h0-\sqrt{R+\overline{x}}\sqrt{R-\overline{x}}$$

how do i find the boundary conditions to satisfy the constants $$\overline{x}$$ and $$C$$?

my boundary conditions are:

$$p = 0 \ @ \ x = R$$
and
$$p = 0 \ @ \ x = -\overline{x} \mbox{ where } \overline{x} \mbox{ is where } \frac{dp}{dx} = 0 \mbox{ (maximum pressure)}$$

i don't know if there is an easy way to do it or not! Thanks for your help!

MT

2. Aug 1, 2009

### HallsofIvy

Staff Emeritus
Well, the obvious thing to do would be to put those conditions into your equation, giving you two equations for $\overline{x}$ and C- except that the conditions say "p= 0" and there is NO p in your equation!

Since your original equation, in terms of integrals, has $\int dp$ on the left side, you should get an equation of the form "p= the integral on the right". I have no idea what the equations you give for h and $\overline{h}$ have to do with that equation!