1. An incompressible fluid of kinematic viscosity v= p/p = 10-4 m²/s flows steadily through a circular pipe of diameter d = 10 cm. The pipe flow is fully developed. If the average velocity V is 2 m/s, is the flow laminar or turbulent? What is the value of the friction factor, f? Friction Factor If the pipe is perfectly smooth on its internal surface and V is 20 m/s, the pipe flow is turbulent (double check yourself). Evaluate its friction factor using the Moody chart below. Repeat (c) by numerically solving the Colebrook formula (using, for example, Matlab). Attach the source code you used. Suppose that the pipe internal surface is rough. Also suppose that increasing V up to 200 m/s yields no change in the value of f found in (a). Determine the relative roughness, e/d, using the Colebrook formula. 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.015 0.01 Laminar Flow Material Concrete, coarse Concrete, new smooth Drawn tubing Glass, Plastic Perspex Iron, cast e (mm) 0.25 0.025 0.0025 0.0025 0.15 3.0 Sewers, old Steel, mortar lined 0.1 Steel, rusted 0.5 Steel, structural or forged 0.025 Water mains, old 1.0 10³ 104 Moody Diagram WEEEEEE Transition Region Complete Turbulence Friction Factor=AP. 105 106 Reynolds Number, Re = PVd Smooth Pipe 107 0.05 0.04 0.03 0.02 0.015 0.01 0.005 0.002 0.001 5x10-4 2x10-4 10-4 5x10-5 10-5 5x10-6 10-6 108 Relative Pipe Roughness