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

Bernouli says that the "total pressure" is concerved for a streamline. But because of frictional losses etc the tot pressure does not stay const. Total pressure consist out of a dynamic pressure an the static pressure. If you get an increase in flow x-section the "static pressure" will increase.

Thank you very much for your response. 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.