Pfriction = Pp + Pf Similarly, the total friction loss, hfriction, as fluid flows through pipes is the sum of the head loss from friction with the pipes, hp, and the head loss from friction through the fittings, hf. hfriction = hp + hf The next two sections describe how to calculate pressure loss due to friction through and fittings. Pressure Loss Due to Friction through Pipes and Ducts Friction Factor Method The pressure loss from friction with the pipes and ducts, Pp, can be calculated from Pp = (f L V2) / (2 D) where f is the friction factor, L is the pipe/duct length, is the fluid density and D is the pipe/duct diameter. An explicit algebraic expression for friction factor, f, was developed by Churchill. This relationship is valid for all ranges of Reynolds numbers. Source: ASHRAE, 2005, pg 2.7. The Reynolds number is: Re = V D / = fluid V D /  where  is the kinematic viscosity (air at 60 F = 0.572 ft2/h and water at 60 F = 0.044 ft2/h), and  is the dynamic viscosity (air at 60 F = 0.043 lbm/h-ft andwater at 60 F = 2.71 lbm/h-ft). The equivalent diameter, De, for a rectangular duct with dimensions L and W is: De = 1.3 (L W)5/8 / (L + W)1/4 Typical values for pipe roughness factors, e, are shown in the figure below.
the upstream velocity Vu to calculate the velocity pressure when calculating head loss through the reducer: hf (in-H20) = kd [Vu (ft/min) / 4,005]2 Source: United McGill, 1990. Example Find the power, Wf, required to push 1,000 cfm of air through 200 ft of 12-inch duct with four 5-gore elbows assuming that 1 and 2 are open to the atmosphere and at the same elevation. P2 = P1 because 1 and 2 are open the atmosphere. V2= V1 because the area of duct at 1 and 2 are the same. z2 = z1 because 1 and 2 are at the same elevation. Thus: hpres = hvel = helev = 0 htotal = hpres + hvel + helev + hp + hf = hp + hf From the monograph, for 1,000 cfm through 12-inch duct, Pduct ~ 0.2 in-H20/100 ft. Hence, the total head loss through the duct is: hp = 0.2 in-H20/100 ft x 200 ft = 0.4 in-H20 The velocity is: V = V / A = 1,000 ft3/min / (3.143 x 12 ft2 / 4) = 1,273 ft/min From the fittings chart, for a 12-inch 5-gore elbow, kf = 0.18. For four elbows, the total head loss is: hf (in-H20) = Nf x kf (V / 4,005)2 where V is in ft/min hf (in-H20) = 4 x 0.18 x (1,273/4,005)2 = 0.073 in-H20 The total head loss through ducts and fittings is: htotal = hp + hf = 0.4 in-H20 + 0.073 in-H20 = 0.473 in-H20
Source: “Monitoring Chiller Plant Performance”, ASHRAE Journal, April, pp. 48-52. Source: “Monitoring Chiller Performance”, ASHRAE Journal, April, pp. 48-52. VSD Fan Retrofits: Example The figure below shows a schematic of VSD retrofit on a constant-volume supply air system in a building. Each box represents a different zone within the building. Each X represents a VAV box, which varies the supply air to maintain zone temperature. The pressure sensor would control the speed of the VSD. References ASHRAE Handbook: Fundamentals, 1977, 1985, 1996, 2005, ASHRAE. Bernier and Bourret, 1999, “Pumping Energy and Variable Frequency Drives”, ASHRAE Journal, December. Pumps, GPM 7-CD, Technical Information. Incropera and DeWitt, 1985, Fundamentals of Heat and Mass Transfer, John and Sons. Kreider and Rabl, 1994, Heating and Cooling of Buildings, McGraw-Hill Inc. Larson, E.D. and Nilsson, L.J., 1991, “Electricity Use and Efficiency in Pumping and Air Handling Systems, ASHRAE Transactions, pgs. 363-377. McQuiston and Parker, 1994, Heating Ventilating and Air Conditioning, John and Sons, Inc. McQuiston, F., Parker, J. and Spitler, J., 2000, “Heating, Ventilating and Air Conditioning: Analysis and Design”. John Wiley and Sons, Inc. Mott, R. L, 2000, Applied Fluid Mechanics, Prentice Hall, Inc.
Nadel, S., Shepard, M., Greenberg, S., Katz, G., and Almeida, A., 1991, “Energy Efficient Motor Systems”, American Counsel for an Energy Efficient Economy, Taylor, S., 2002, “Primary-Only vs. Primary Secondary Variable Flow Systems”, ASHRAE Journal, February, 2002, pgs 25-29. Tutterow, 199x, Energy Efficient Fan Systems, Industrial Energy Technology Conference, United McGill, 1990, Engineering Design Reference Manual. Department of Energy, 2002m “Pumping Systems Field Monitoring and Application of the Pumping System Assessment Tool PSAT”,