Problem 4. (25 points) Consider incompressible flow in the entrance of a circular tube having radius R. The inlet flow is uniform, u₁ = U₁. The flow at section 2 is turbulent, fully-developed pipe flow having a velocity profile of u₂(r) = UCL r 1/7 . In R your solution, you need to work out the entire analysis starting with the conservation of mass and momentum equations from Lesson F.3 Slide 2. d ƒ (√ſſ cv p dV ) + ſſ ¸ P (V • ñ) dA dt JCV 0 = ΣΕ = d dt ρ CS ç ( §ſſ cv pv dV ) + ſſ ¸ П ( V •ñ) dA CS u₁ =U₁ =UCL a (1-7) " r CL a. Use conservation of mass to find UC as a function (multiple) of U.. (Ans: 60/49 U b. Find the wall drag force F between the inlet and location 2 as a function of P, PP, U, R. Hint: Use the substitution u=1-r/R to integrate. Show all work in the integration. Do not use an integration table or online solver. c. Find the momentum-flux correction factor for the velocity profile at location 2. Give the correction factor as a fraction and decimal. Hint: You can find this value from your calculations in Part b.