Question

Please answer the following question using the numerical iteration method and show all steps! Thank you!

Problem 1 A duct with diameter D, surface roughness ε, and length L = 1500 feet transports air with specific weight Yair = 0.0752 lbs/ft' at volume flow rate of Q = 9000 ft/min. A pressure gradient of Ap/L is measured in inch of water per 1500 feet of duct. Use either a graphical method (preferred) or a numerical iteration method to fill out the table below. Show all steps. If you choose to use a graphical method, show a Moody's chart and how you derive your answer. Pipe diameter D (ft) Flow velocity V (ft/s) Pressure gradient Ap /L (inches of H20 per 1500' pipe) 1.50 Surface roughness & (ft) 3.0 21 ? (a) (b) 3.0 21 ? 0.012 (C) 3.0 ? 1.50 0.012 (d) ? 21 1.50 0.012

Answer 1

given that L= 1500 feet 0.752 lbs/ft² 9000 ft/mi Quir min & D = 3.0 feet (given) Area TTD² 4. 3.14 X 3x3 = 7.06 pt² 4 9000 4 150 oft/sec 60 @ flow relocity (V) = 150 7.06 A = 21:24 ft/s d. Again, we have, V= 2lot ft/s So @VA A = V D 2 TD 4 4 X de 150 214 3.14 VT V 3.01 ft

3.98 x 10-3 an the sa relative surface roughness D 0.012 3.01 surface Roughness (6) = (Relative surface Roughness) x D = 3.988 10 3 x 3 0.0119 ft inch of Hooper 1500 feet 6 Pressure gradient