MAE305_pset03s

MAE305_pset03s - M&AE 3050 Problem Set 3 Fa 2009 Solution...

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M&AE 3050 Problem Set 3 Fa 2009 Solution For the problems below, assume all ﬂows can be approximated as incompressible . 1. Consider the incompressible ﬂow of water through a divergent duct. The inlet velocity and area are 5 ft/s and 10 ft 2 , respectively. (a) If the exit area is 4 times the inlet area, calculate the water ﬂow velocity at the exit. (b) Calculate the pressure di±erence between the exit and the inlet. The density of water is 62.4 lb m /ft 3 . Solution (a) Let A 1 be the inlet area and A 2 be the outlet area. Continuity requires ρv 1 A 1 = ρv 2 A 2 . Solving for v 2 yields v 2 = v 1 ± A 1 A 2 ² =5 ± 1 4 ² =1 . 25 ft / s . (b) The incompressible Bernoulli equation is p 1 + 1 2 ρv 2 1 = p 2 + 1 2 ρv 2 2 . Solving for the pressure di±erence yields p 2 - p 1 = 1 2 ρ ( v 2 1 - v 2 2 ) =(0 . 5)(62 . 4 / 32 . 2)(5 2 - 1 . 25 2 )=22 . 7lb / ft 2 . 2. An open circuit suction wind tunnel has a fan at the exit that draws air. The ratio of the inlet cross sectional area to the cross section of the test section is 9:1. Assume

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MAE305_pset03s - M&AE 3050 Problem Set 3 Fa 2009 Solution...

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