In order to properly size the fan required for a heating and air conditioning system, the pressure drop in the system must be determined. Consider the air distribution system shown in Figure P4.29. Dry air at 65°F, 1 atm enters the main duct of the system at 2250 cfm. There are two take-offs in the main duct where 750 cfm of air are used for individual room air conditioning. The remaining air travels down the main duct and is eventually distributed to a third room. All ducts are circular and the duct diameters are sized such that the velocity in each section of the main distribution duct is the same. The fittings that provide the required diameter reduction are 30° tapered reducers. The absolute roughness of a galvanized steel duct is 0.0005 ft. For this air distribution system, determine,

a. The diameters of the second and third sections of the main duct (D2 and D3)

b. The total pressure drop in the main duct from A to B, expressed in inches of water (in H2O).

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2250 cfm A FIGURE P4.29 An air distribution system. L = 50 ft D = 1.5 ft 750 cfm D 750 cfm L = 60 ft D3 L3=40 ft