Questions on a pressure profile
 

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

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.