FIGURE Q2a, Q2b and Q2c show the laminar flow of an incompressible Newtonian liquid in an inclined cylindrical pipe. Assume L is considerably larger than the diameter of the pipe. Using shell balance method, develop the velocity distribution profile for the liquid flowing in the cylindrical pipe based on the information provided in TABLE Q2. Using the developed velocity profile, estimate the maximum velocity (m/s) of the liquid if the inlet static pressure, outlet static pressure, liquid density and viscosity are P0, PL, and , respectively. Given that the length and radius of the cylinder are L and R, respectively

properties of cylinder : P0 = 100,000 Pa PL= 20,000 Pa = 0.001 kg/(m.s) = 1000 kg/m3 L = 10 m R = 0.005 m = 45 (50 marks)

Direction of flow Direction of flow Gravity FIGURE Q2a: Schematic diagram of an incompressible Newtonian liquid flowing in an inclined cylindrical pipe. Direction of flow Direction of flow Gravity FIGURE Q2a: Schematic diagram of an incompressible Newtonian liquid flowing in an inclined cylindrical pipe