Ethanol flows down a pipe with a very large rectangular section. The pipe is solid and inclined $45$ degrees downwards from the horizontal. The height $($h$)$ of the pipe is $30$ cm$.$ The flow is fully developed and in steady state. The viscosity and density of ethanol are constant and ethanol is a Newtonian fluid.

Determine:

a$)$ The relationship between the shear stress $($Tau xz$)$ and x

b$)$ The value of the shear stress $($Tau xz$)$ at the top wall of the pipe.

Information for part b$)$:

density of ethanol $=789$ kg$/$m$^3$

pressure gradient $($pressure drop$)=5000$ Pa