Answer to Question #178424 in Mechanical Engineering for Johan Nieuwoudt

Question

Given that oil, with a density p = 700 kg/m3 and Kinematic viscosity v = 0.00001m2/s flows at 0.3m3/s through 500m of 250mm diameter cast iron pipe and the roughness of cast iron pipe e = 0.26mm

Take note that the pipe runs at an angle of 10ndegrees

• Determine the Reynolds number
• The friction factor f
• The head loss due to friction

Answer 1

Velocity of flow, V = Q/A = Q/($\pi$/4 x D²) = 0.3 m³/s / (3.14/4 x (0.25 m)²) = 6.11 m/s

Reynolds number, Re = VD/$\upsilon$ = (6.11 m/s x 0.25 m) / 0.00001 m²/s = 152 750

The Reynolds number is greater than 2000. So the flow is turbulent. 

Friction factor for turbulent flow, f = [1.14 + 2log(D/e)]^-2 = [1.14 + 2log(0.25/0.00026)]^-2 = 0.0198

Head loss, H_L = f(L/D)(V²/2g) = 0.0198(500 m/0.25 m)((6.11 m/s)²/(2 x 9.81 m/s²) = 75.35 m