Explanation Write the expression for the temperature ratio for an isentropic process. T 1 T 2 = ( p 1 p 2 ) k − 1 k (I) Here, temperature at station 1 is T 1 , pressure at station 1 is p 1 , temperature at station 2 is T 2 , pressure at station 2 is p 2 and the ratio of specific heats is k . Write the expression for the velocity of sound at station 1 ( c 1 ) . c 1 = k R T 1 (II) Here, the specific gas constant of air is R . Write the expression for Mach number at station 1 ( Ma 1 ) . Ma 1 = V 1 c 1 (III) Write the expression to find the density of air at station 1 ( ρ 1 ) ρ 1 = p 1 R T 1 (IV) Write the expression for the mass flow rate ( m ˙ 1 ) m ˙ 1 = ρ 1 A 1 V 1 (V) Here, area at station 1 is A 1 Conclusion: Substitute, 225 K for T 2 , 4 atm for p 1 , 2 atm for p 2 and 1.4 for k in Equation (I). T 1 = 225 K ( 4 atm 2 atm ) 1.4 − 1 1.4 T 1 = 274.3 K Substitute, 1.4 for k , 287 N ⋅ m kg ⋅ K for R and 274.3 K for T 1 in Equation (II). c 1 = 1.4 ( 287 N ⋅ m kg ⋅ K ) ( 274.3 K ) c 1 = 332 m s Substitute, 40 m s for V 1 and 332 m s for c 1 in Equation (III)

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Question

Chapter 11.6, Problem 37P

To determine

The flowrate and the Mach number at both the stations.

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Chapter 11 Solutions

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

Ch. 11.1 - Prob. 1P Ch. 11.1 - Air flows steadily between two sections in a duct....Ch. 11.1 - Consider the flow process in Fig. P11.3. Does the...Ch. 11.1 - Prob. 4P Ch. 11.1 - Prob. 5P Ch. 11.1 - Prob. 6P Ch. 11.1 - Prob. 7P Ch. 11.1 - Prob. 8P Ch. 11.1 - Air flows in a 15-cm-diameter horizontal pipe. At...Ch. 11.1 - An air heater in a large coal-fired steam...

Ch. 11.2 - Determine the static pressure to stagnation...Ch. 11.2 - Prob. 12P Ch. 11.2 - Prob. 13P Ch. 11.2 - Prob. 14P Ch. 11.2 - Prob. 15P Ch. 11.3 - Prob. 16P Ch. 11.3 - Prob. 17P Ch. 11.3 - Prob. 18P Ch. 11.3 - Prob. 19P Ch. 11.3 - Prob. 20P Ch. 11.3 - Prob. 21P Ch. 11.3 - Prob. 22P Ch. 11.4 - Prob. 23P Ch. 11.4 - Prob. 24P Ch. 11.4 - Prob. 25P Ch. 11.4 - Prob. 26P Ch. 11.4 - Prob. 27P Ch. 11.4 - Air flows in a constant-area, insulated duct. The...Ch. 11.5 - Prob. 29P Ch. 11.5 - The Pitot tube on a supersonic aircraft (see Video...Ch. 11.5 - An aircraft cruises at a Mach number of 2.0 at an...Ch. 11.5 - Prob. 32P Ch. 11.5 - Prob. 33P Ch. 11.5 - Prob. 34P Ch. 11.5 - Prob. 35P Ch. 11.6 - The stagnation pressure and temperature of air...Ch. 11.6 - Prob. 37P Ch. 11.6 - Prob. 38P Ch. 11.6 - Prob. 39P Ch. 11.6 - Prob. 40P Ch. 11.6 - Prob. 41P Ch. 11.6 - The static pressure to stagnation pressure ratio...Ch. 11.7 - Air flows steadily and isentropically from...Ch. 11.7 - Prob. 44P Ch. 11.7 - Prob. 45P Ch. 11.7 - Prob. 46P Ch. 11.7 - At a certain point in a pipe, air flows steadily...Ch. 11.7 - Prob. 48P Ch. 11.7 - Prob. 49P Ch. 11.7 - Prob. 50P Ch. 11.7 - A jet engine is to be designed for an altitude of...Ch. 11.7 - Prob. 52P Ch. 11.7 - A convergent–divergent nozzle has an exit throat...Ch. 11.7 - An ideal gas flows isentropically through a...Ch. 11.8 - Standard atmospheric air (T0 = 59 F, p0 = 14.7...Ch. 11.8 - Prob. 57P Ch. 11.8 - Prob. 58P Ch. 11.8 - Prob. 59P Ch. 11.8 - Prob. 64P Ch. 11.9 - Prob. 66P Ch. 11.9 - Prob. 67P Ch. 11.9 - Prob. 68P Ch. 11.9 - Air enters a frictionless, constant area duct with...Ch. 11.9 - Prob. 70P Ch. 11.9 - Prob. 71P Ch. 11.9 - Prob. 72P Ch. 11.9 - Prob. 73P

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