BERNOULLI’S EQUATION Fluid FlowMost techniques for evaluating head loss due to friction are empirical (based almost exclusivelyon experimental evidence) and are based on a proportionality constant called the friction factor(f), which will be discussed in the next section.Example: Extended BernoulliWater is pumped from a large reservoir to a point 65 feet higher than the reservoir. Howmany feet of head must be added by the pump if 8000 lbm/hr flows through a 6-inch pipeand the frictional head loss is 2 feet? The density of the fluid is 62.4 lbm/ft^{3}, and thecross-sectional area of a 6-inch pipe is 0.2006 ft^{2}.Solution:To use the modified form of Bernoulli’s equation, reference points are chosen at thesurface of the reservoir (point 1) and at the outlet of the pipe (point 2). The pressure atthe surface of the reservoir is the same as the pressure at the exit of the pipe, i.e.,atmospheric pressure. The velocity at point 1 will be essentially zero.Using the equation for the mass flow rate to determine the velocity at point 2:m_{2}rA2v2v_{2}m_{2}rA2v_{2}8000^{lbm}hr62.4^{lbm}ft^{3}(0.2006 ft^{2})v_{2}639fthr1 hr3600 secv_{2}0.178ftsecHT-03 Page 26 Rev. 0