Question: How to give a boundary condition as 'finite' ?

Dear community,

I am new to maple and was trying to get a solution for simple Hagen Poiseuille Flow. Hagen Poiseuille Flow  has governing equation as :

ode2 := -v+mu((diff(r*(diff(ur), r)), r))/r) = 0

here 'v' is a constant (pressure gradient) and the equation is in cylindrical coordinates

the problem has two boundary conditions as u(R) = 0 and u(0) = 'finite'.

I am struck at the second condition as there seems to be no option to say maple that the solution should be finite at a point.

Can anyone help me in this regard?

 

 

Alternatively, I can give second boundary condition as (D(u))(0) = 0. However, this gives a solution as follows:

dsolve({ode2, u(R) = 0, (D(u))(0) = 0}, u(r)):

u(r) = (1/4)*RootOf(-mu(_Z)+v)*r^2-(1/4)*RootOf(-mu(_Z)+v)*R^2

 

This doesn't look very easy, and I don't know what to do with this. 

The solution for the above differential equation is simple and can be obtained on paper. Please help.

 

Thank you.

 

 

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