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(Solved): 2.2 (a) Determine the equivalent rectangular shaped duct sizes for the duct lay-out as shown below ...
2.2 (a) Determine the equivalent rectangular shaped duct sizes for the duct lay-out as shown below using equal friction method. The height of the duct should not exceed 24 " and also the maximum velocity in the main trunk should not exceed . Assume that the pressure drop across each outlet diffuser to be 0.03 " of wg and for the filter " of wg), heating " of wg), cooling coils " of wg) and an equivalent length for 15' for elbows, 12' for main flow in Tees, and ' for branch flow in Tees. The numbers in circles denote the station points in the circuit. F. filter: HC-heating coil, CC-cooling coil (b) Determine the size of the fan to be employed for the duct system and also determine the speed, shaft power and the total head developed by the fan. (c) Show where you would install the dampers in order to balance the duct system. (30 pts)
Expert Answer
(a) The equivalent rectangular duct sizes can be determined using the equal friction method which involves maintaining a constant friction loss per unit length of duct. The first step is to calculate the equivalent length of each fitting: - Elbow: 15 ft equivalent length - Main flow Tee: 12 ft equivalent length - Branch flow Tee: 40 ft equivalent length - Filter: 0.08 " wg pressure drop = 8.3 ft equivalent length - Heating coil: 0.24 " wg pressure drop = 24.9 ft equivalent length - Cooling coil: 0.23 " wg pressure drop = 23.9 ft equivalent length - Outlet diffuser: 0.03 " wg pressure drop = 3.1 ft equivalent length Next, we can calculate the total equivalent length for each branch of the circuit: - Branch A: 2(20) + 2(15) + 2(12) + 8.3 + 24.9 + 3.1 = 118.3 ft - Branch B: 2(30) + 2(15) + 2(12) + 23.9 + 3.1 = 126.1 ft - Branch C: 2(30) + 2(15) + 2(12) + 8.3 + 23.9 + 3.1 = 128.6 ft - Branch D: 2(20) + 2(15) + 2(12) + 23.9 + 3.1 = 117.1 ft We can now use the equivalent length and the maximum velocity constraint to determine the cross-sectional area of each duct branch: - Branch A: (118.3 ft / 1200 fpm) * (144 in^2 / ft^2) = 14.8 in^2 -> equivalent rectangular duct size of 4" x 18" - Branch B: (126.1 ft / 1200 fpm) * (144 in^2 / ft^2) = 15.8 in^2 -> equivalent rectangular duct size of 4" x 20" - Branch C: (128.6 ft / 1200 fpm) * (144 in^2 / ft^2) = 16.1 in^2 -> equivalent rectangular duct size of 4" x 21" - Branch D: (117.1 ft / 1200 fpm) * (144 in^2 / ft^2) = 14.6 in^2 -> equivalent rectangular duct size of 4" x 18".