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I finally figured out how to solve the integral:

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

using maple and have it export to matlab where:

[tex]h=R+h0-\sqrt{R+x}\sqrt{R-x}[/tex]

[tex]\overline{h}=R+h0-\sqrt{R+\overline{x}}\sqrt{R-\overline{x}}[/tex]

how do i find the boundary conditions to satisfy the constants [tex]\overline{x}[/tex] and [tex]C[/tex]?

my boundary conditions are:

[tex]p = 0 \ @ \ x = R[/tex]

and

[tex]p = 0 \ @ \ x = -\overline{x} \mbox{ where } \overline{x} \mbox{ is where } \frac{dp}{dx} = 0 \mbox{ (maximum pressure)}[/tex]

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

MT

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# Solving an equation with boundary conditions

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