1. Starting from Navier-Stokes equations derive the algebraic expression describing the fully developed velocity profile in a circular pipe of radius R; assume laminar, developed, steady, unidirectional, isothermal flow.

a) Derive the differential equation by reducing Navier-Stokes equations to this case and state all needed boundary conditions.

b) Solve the mathematical model obtained in part (a) analytically.

c) Plot the obtained solution (algebraic expression) for the velocity profile obtained in (b) above in an Excel sheet. Please label properly the obtained graph. Ineligible graphs will not be graded. To create a graph for the solution you have to adopt some realistic values for fluid properties and the pipe. Here is the suggested data: