[saisanthoshm88]

I have some questions on a pressure profile obtained from a simple 2D laminar pipe flow.

Please look into the attached .jpg image of the pressure contour

Could some one please provide clarifications to the following questions I have -

As the flow proceeds from the inlet, there is a gradual pressure drop. Could this be solely attributed to the frictional losses due to wall shear ?

The bernoullis theorem doesn’t seem to hold good here because it is expected that the pressure should increase as the cross sectional area increases for the flow, however a pressure drop is witnessed from the plot. Could you please explain the limitation of bernoullis theorem in this case

[saisanthoshm88]

Sorry this question is rather academic. I've gone through some books and found that it's a case of Poiseuille flow. Bernoullis theorem is not applicable here as it is a viscous flow (the flow has a very low reynolds number so the viscous effects dominate the inertia). Yes the pressure drop is due to the viscous shear , the shear stress acts in a direction opposite to the flow and a pressure drop from inlet to outlet is required to counter balance this.