Solving 1st Order ODE for Laminar Flow: A Simple Guide | Jerome, Engineer

[plasticpigeon]

Hello people

I am an engineer and therefore not a great mathematician.

To solve a problem involving laminar flow i need to solve the equation with a general form

dp/dx + A/p - B = 0 which I don't know how to do.

Can anyone shed any light on how to solve this simple looking problem.

Many thanks

Jerome

 

[CompuChip]

For B = 0 the solution can be written as
$$p^2 = - 2 A x + c$$

For B not equal to 0, Mathematica gives something with a ProductLog, so there is probably no nice solution, except for special values of A and B.

 

[defunc]

Seperation of variables gives you the implicit solution

p+(A/B)ln(Bp-A)=Bx + constant.

 

[plasticpigeon]

Dear Defunc

Many thanks for your reply. I'd be very grateful if you could explain to me how you got the solution. I could not see how to separate variables because of the constant term B.

Many thanks

Jerome

 

[defunc]

You can separate it to obtain te following:


p/(Bp-A) dp=dx.

 

[plasticpigeon]

thanks, that has helped me a lot!