Explanation Given: Temperature of air inside the tank ( T 0 ) is 100 ° F . Pressure of air inside the tank ( p 0 ) is 50 psia. Inlet area of the nozzle ( A 1 ) is 10 in . 2 Exit area of the nozzle ( A 2 ) is 1 in . 2 Calculation: Check for choking. p b p 0 = 14.7 50 = 0.294 < 0.528 The flow is choked and thus the Mach number at exit of the nozzle is 1 . Determine the pressure at exit. p 2 p 0 = 0.528 p 2 50 psi = 0.528 p 2 = 26.4 psi Determine the temperature at exit. T 0 T 2 = 1 + k − 1 2 M 2 2 560 K T 2 = 1 + 1.4 − 1 2 ( 1 ) 2 T 2 = 466.66 ° R Determine the density at exit. ρ 2 = p 2 R T 2 = 26.4 psi ( 12 in . 1 ft ) 2 53.34 ft ⋅ lbf / lbm ⋅ ° R × 466.66 ° R = 0.1537 lbm / ft 3 Determine the velocity at exit. V 2 = M 2 c 2 V 2 = M 2 k R T 2 V 2 = 1 × 1.4 × 53.34 ft ⋅ lbf / lbm ⋅ ° R × 466

Fox and McDonald's Introduction to Fluid Mechanics

9th Edition

ISBN: 9781118912652

Author: Philip J. Pritchard, John W. Mitchell

Publisher: WILEY

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Chapter 12, Problem 75P

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Fox and McDonald's Introduction to Fluid Mechanics

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Solution Summary: The author calculates the Mach number at exit of the nozzle.

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