HEAD LOSSFluid FlowThe quantity used to measure the roughness of the pipe is called the relative roughness, whichequals the average height of surface irregularities (e) divided by the pipe diameter (D).Relative RoughnesseDThe value of the friction factor is usually obtained from the Moody Chart (Figure B-1 ofAppendix B). The Moody Chart can be used to determine the friction factor based on theReynolds number and the relative roughness.Example:Determine the friction factor (f) for fluid flow in a pipe that has a Reynolds number of40,000 and a relative roughness of 0.01.Solution:Using the Moody Chart, a Reynolds number of 40,000 intersects the curve correspondingto a relative roughness of 0.01 at a friction factor of 0.04.Darcy’sEquationThe frictional head loss can be calculated using a mathematical relationship that is known asDarcy’s equation for head loss. The equation takes two distinct forms. The first form of Darcy’sequation determines the losses in the system associated with the length of the pipe.(3-14)H_{f}fL v^{2}D 2 gwhere:f = friction factor (unitless)L = length of pipe (ft)D = diameter of pipe (ft)v = fluid velocity (ft/sec)g = gravitational acceleration (ft/sec^{2})Example: Darcy’s Head Loss EquationA pipe 100 feet long and 20 inches in diameter contains water at 200°F flowing at a massflow rate of 700 lbm/sec. The water has a density of 60 lbm/ft^{3} and a viscosity of 1.978x 10^{-7} lbf-sec/ft^{2}. The relative roughness of the pipe is 0.00008. Calculate the head lossfor the pipe.HT-03 Page 32 Rev. 0

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