2 replies to this topic

[Engineer in making]

Hi everyone,

 

I'm trying to solve a fluid problem for isothermal, steady, unidirectional laminar flow of an incompressible non-Newtonian. And was asked to solve the navier stokes equation ( Momentum equation) for it. Here's the diagram:

 

http://prntscr.com/5bwfli

 

Shear stress formula :

http://prntscr.com/5bwful

 

Mementum equation:

http://prntscr.com/5bwdbu

My solution: 

http://prntscr.com/5bweal

 

I'm just wondering If my approach for the problem and my solution was right since I'm having doubts about my solution. 

 

 

 

[breizh]

http://en.wikipedia....tokes_equations

Hi,

 

 

Hope this  helps

 

Good luck

Breizh

Edited by breizh, 01 December 2014 - 01:21 AM.

[ahmadikh]

 Hello,

 

Navier-Stokes equation in X direction should be used to achieve the velocity profile...As stated in the attachment provided by Breizh, remember that for non-Newtonian fluids, the type of fluid should be known in order to determine the shear stress change as a function of velocity gradient.

 

The pressure gradient term (dP/dx) in X direction is missing in your equation. Assuming the following assumption your solution is fine, except the pressure gradient term is missing:

 

1) There is no motion in Y and Z direction (Uy = Uz = 0)

2) Ux is only function of Y (dUx/x = 0)

3) Steady State Condition (dUx/dt = 0)

4) There is no velocity gradient in X and Z direction, so no shear stress (Txz = Txx = 0)

 

Hope this helps...

 

Best,

Milad