I'm trying to solve Bernoulli equation in differential form.

I'm trying to solve this bernoulli equation.

(∂u/∂t)+ρ(u∂u/∂x)=-∂p/∂x+(μ∂^2 u)/(∂x^2 )

after assuming the variation of u with time is zero and ignoring viscous effects, I got to ρ(u∂u/∂x)=-∂p/∂x

by solving this, i wish to get value of u for different values of dx( variation of u along a straight line ) for some constant value of p. But to do this i need to convert this equation to the form required by matlab, which im not able to do.At the end I need to plot the variation of u against dx. How can i achieve this?

Answer 1

[Alan Stevens]

If p is constant then dp/dx = 0, hence du/dx = 0, which means u is constant.

If you meant the pressure gradient is constant then u*du/dx = -(p/dx)/rho = constant, or du^2/dx = -2(dp/dx)/rho, so u^2 = (-2(dp/dx)/rho)*x + uo^2, where uo is the value of u when x = 0.

[suresh berike]

how did you get du^2/dx from u*du/dx? I think its not possible. Also, how did you get 2 on the right hand side of the equation?

[Alan Stevens]

du^2/dx = 2udu/dx so udu/dx = (1/2)du^2/dx. I then multiplied both sides by 2.

[suresh berike]

Ok thanks a lot for the help.