Viscous drag on the walls of a pipe

Question

Assignment:

For laminar flow in the entrance of to a pipe, as shown in figure, the entrance is uniform u=U₀, and the flow downstream is parabolic in profile u(r)=C(r₀²-r²). Using integrla relations, show that the viscous drag exerted on the pipe walls between 0 and x is given by

Drag = πr₀² (p₀ - p_x -1/3pU_o²)

Provide complete and step by step solution for the question and show calculations and use formulas.