Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
9th Edition
ISBN: 9781259822674
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Chapter 17.7, Problem 121RP
To determine

The expressions for the ratio of the stagnation pressure after a shock wave to the static pressure before the shock wave as a function of k and the Mach number upstream of the shock wave Ma1.

Expert Solution & Answer
Check Mark

Answer to Problem 121RP

The expressions for the ratio of the stagnation pressure after a shock wave to the static pressure before the shock wave as a function of k and the Mach number upstream of the shock wave Ma1 is obtained and shown in Equation (VI).

Explanation of Solution

Write the Equation 17-38 as in text book (the relation between the pressures after shock and before shock for an ideal gases).

P2P1=1+kMa121+kMa22 (I)

Here, the specific heat ratio is k, the Mach number is Ma, the subscript 1 and 2 indicates the states of before and after shocks.

Write the relation between the stagnation pressure (P0) and static pressure (P) for ideal gas at isentropic flow.

P0P=[1+(k12)Ma2]kk1 (II)

Here, the subscript 0 indicates the stagnation state.

Write the Equation 17-39 as in text book (the expression for Mach number after shock).

Ma22=Ma12+2/(k1)2Ma12k/(k1)1 (III)

Conclusion:

Rearrange the Equation (I) to obtain P2.

P2=P1(1+kMa121+kMa22)

Express the Equation (II) for state 2 i.e. after shock.

P02P2=[1+(k12)Ma22]kk1 (IV)

Substitute P1(1+kMa121+kMa22) for P2 in Equation (IV)

P02P1(1+kMa121+kMa22)=[1+(k12)Ma22]kk1P02P1=(1+kMa121+kMa22)[1+(k12)Ma22]kk1 (V)

Refer Equation (III).

Substitute Ma12+2/(k1)2Ma12k/(k1)1 for Ma22 in Equation (V).

P02P1=(1+kMa121+k(Ma12+2/(k1)2Ma12k/(k1)1))[1+(k12)(Ma12+2/(k1)2Ma12k/(k1)1)]kk1=(1+kMa12[2Ma12k/(k1)1]+[kMa12+k2/(k1)]2Ma12k/(k1)1)[1+(k1)[Ma12+2/(k1)]2(2Ma12k/(k1)1)]kk1=((1+kMa12)(2Ma12k/(k1)1)2Ma12k/(k1)1+kMa12+k2/(k1))[1+(k1)Ma12+22(2Ma12k/(k1)1)]kk1=((1+kMa12)(1k1)(2Ma12k1(k1))2Ma12k/(k1)1+kMa12+k2/(k1))[1+2[(k1)Ma12/2+1]2(2Ma12k/(k1)1)]kk1

=((1+kMa12)(2Ma12kk+1)(k1)[2Ma12k/(k1)1+kMa12+k2/(k1)])[1+(k1)Ma12/2+12Ma12k/(k1)1]kk1=((1+kMa12)(2Ma12kk+1)2Ma12k1(k1)+(k1)kMa12+2k)[1+(k1)Ma12/2+12Ma12k/(k1)1]kk1=((1+kMa12)(2Ma12kk+1)2Ma12kk+1+k2Ma12kMa12+2k)[1+(k1)Ma12/2+12Ma12k/(k1)1]kk1=((1+kMa12)(2Ma12kk+1)2Ma12k+k2Ma12kMa12k+1+2k)[1+(k1)Ma12/2+12Ma12k/(k1)1]kk1

=((1+kMa12)(2Ma12kk+1)kMa12(2+k1)+k+1)[1+(k1)Ma12/2+12Ma12k/(k1)1]kk1=((1+kMa12)(2Ma12kk+1)kMa12(k+1)+k+1)[1+(k1)Ma12/2+12Ma12k/(k1)1]kk1 (VI)

Thus, the expressions for the ratio of the stagnation pressure after a shock wave to the static pressure before the shock wave as a function of k and the Mach number upstream of the shock wave Ma1 is obtained and shown in Equation (VI).

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Consider a hypersonic vehicle with a spherical nose flying at Mach 20at a standard altitude of 150,000 ft, where the ambient temperature andpressure are 500◦R and 3.06 lb/ft2, respectively. At the point on thesurface of the nose located 20◦ away from the stagnation point, estimatethe: (a) pressure, (b) temperature, (c) Mach number, and (d) velocity ofthe flow.
Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.5. If the pressure and temperature of air are 10.0 psia and 440.5 R, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock. Compare these results to those for helium undergoing a normal shock under the same conditions.
An ideal isentropic nozzle is attached to an infinite reservoir that has stagnation conditions 3 MPa and 2250 K, and a constant specific heat of 1.2. If the nozzle's static exit pressure is 38.871 kPa, what is the exit static temperature? Also determine the nozzle's exit Mach number, stagnation pressure, and stagnation temperature.

Chapter 17 Solutions

Thermodynamics: An Engineering Approach

Ch. 17.7 - Prob. 11PCh. 17.7 - Prob. 12PCh. 17.7 - Prob. 13PCh. 17.7 - Prob. 14PCh. 17.7 - Prob. 15PCh. 17.7 - Prob. 16PCh. 17.7 - Prob. 17PCh. 17.7 - Prob. 18PCh. 17.7 - Prob. 19PCh. 17.7 - Prob. 20PCh. 17.7 - Prob. 21PCh. 17.7 - Prob. 22PCh. 17.7 - Prob. 23PCh. 17.7 - Prob. 24PCh. 17.7 - Prob. 25PCh. 17.7 - Prob. 26PCh. 17.7 - The isentropic process for an ideal gas is...Ch. 17.7 - Is it possible to accelerate a gas to a supersonic...Ch. 17.7 - Prob. 29PCh. 17.7 - Prob. 30PCh. 17.7 - A gas initially at a supersonic velocity enters an...Ch. 17.7 - Prob. 32PCh. 17.7 - Prob. 33PCh. 17.7 - Prob. 34PCh. 17.7 - Prob. 35PCh. 17.7 - Prob. 36PCh. 17.7 - Prob. 37PCh. 17.7 - Air at 25 psia, 320F, and Mach number Ma = 0.7...Ch. 17.7 - Prob. 39PCh. 17.7 - Prob. 40PCh. 17.7 - Prob. 41PCh. 17.7 - Prob. 42PCh. 17.7 - Prob. 43PCh. 17.7 - Is it possible to accelerate a fluid to supersonic...Ch. 17.7 - Prob. 45PCh. 17.7 - Prob. 46PCh. 17.7 - Prob. 47PCh. 17.7 - Consider subsonic flow in a converging nozzle with...Ch. 17.7 - Consider a converging nozzle and a...Ch. 17.7 - Prob. 50PCh. 17.7 - Prob. 51PCh. 17.7 - Prob. 52PCh. 17.7 - Prob. 53PCh. 17.7 - Prob. 54PCh. 17.7 - Prob. 57PCh. 17.7 - Prob. 58PCh. 17.7 - Prob. 59PCh. 17.7 - Prob. 60PCh. 17.7 - Prob. 61PCh. 17.7 - Air enters a nozzle at 0.5 MPa, 420 K, and a...Ch. 17.7 - Prob. 63PCh. 17.7 - Are the isentropic relations of ideal gases...Ch. 17.7 - What do the states on the Fanno line and the...Ch. 17.7 - It is claimed that an oblique shock can be...Ch. 17.7 - Prob. 69PCh. 17.7 - Prob. 70PCh. 17.7 - For an oblique shock to occur, does the upstream...Ch. 17.7 - Prob. 72PCh. 17.7 - Prob. 73PCh. 17.7 - Prob. 74PCh. 17.7 - Prob. 75PCh. 17.7 - Prob. 76PCh. 17.7 - Prob. 77PCh. 17.7 - Prob. 78PCh. 17.7 - Prob. 79PCh. 17.7 - Air flowing steadily in a nozzle experiences a...Ch. 17.7 - Air enters a convergingdiverging nozzle of a...Ch. 17.7 - Prob. 84PCh. 17.7 - Prob. 85PCh. 17.7 - Consider the supersonic flow of air at upstream...Ch. 17.7 - Prob. 87PCh. 17.7 - Prob. 88PCh. 17.7 - Air flowing at 40 kPa, 210 K, and a Mach number of...Ch. 17.7 - Prob. 90PCh. 17.7 - Prob. 91PCh. 17.7 - Prob. 92PCh. 17.7 - What is the characteristic aspect of Rayleigh...Ch. 17.7 - Prob. 94PCh. 17.7 - Prob. 95PCh. 17.7 - What is the effect of heat gain and heat loss on...Ch. 17.7 - Consider subsonic Rayleigh flow of air with a Mach...Ch. 17.7 - Prob. 98PCh. 17.7 - Prob. 99PCh. 17.7 - Air is heated as it flows subsonically through a...Ch. 17.7 - Prob. 101PCh. 17.7 - Prob. 102PCh. 17.7 - Prob. 103PCh. 17.7 - Air enters a rectangular duct at T1 = 300 K, P1 =...Ch. 17.7 - Prob. 106PCh. 17.7 - Prob. 107PCh. 17.7 - Air is heated as it flows through a 6 in 6 in...Ch. 17.7 - What is supersaturation? Under what conditions...Ch. 17.7 - Steam enters a converging nozzle at 5.0 MPa and...Ch. 17.7 - Steam enters a convergingdiverging nozzle at 1 MPa...Ch. 17.7 - Prob. 112PCh. 17.7 - Prob. 113RPCh. 17.7 - Prob. 114RPCh. 17.7 - Prob. 115RPCh. 17.7 - Prob. 116RPCh. 17.7 - Prob. 118RPCh. 17.7 - Prob. 119RPCh. 17.7 - Using Eqs. 174, 1713, and 1714, verify that for...Ch. 17.7 - Prob. 121RPCh. 17.7 - Prob. 122RPCh. 17.7 - Prob. 123RPCh. 17.7 - Prob. 124RPCh. 17.7 - Prob. 125RPCh. 17.7 - Prob. 126RPCh. 17.7 - Nitrogen enters a convergingdiverging nozzle at...Ch. 17.7 - An aircraft flies with a Mach number Ma1 = 0.9 at...Ch. 17.7 - Prob. 129RPCh. 17.7 - Helium expands in a nozzle from 220 psia, 740 R,...Ch. 17.7 - Helium expands in a nozzle from 0.8 MPa, 500 K,...Ch. 17.7 - Air is heated as it flows subsonically through a...Ch. 17.7 - Air is heated as it flows subsonically through a...Ch. 17.7 - Prob. 134RPCh. 17.7 - Prob. 135RPCh. 17.7 - Air is cooled as it flows through a 30-cm-diameter...Ch. 17.7 - Saturated steam enters a convergingdiverging...Ch. 17.7 - Prob. 138RPCh. 17.7 - Prob. 145FEPCh. 17.7 - Prob. 146FEPCh. 17.7 - Prob. 147FEPCh. 17.7 - Prob. 148FEPCh. 17.7 - Prob. 149FEPCh. 17.7 - Prob. 150FEPCh. 17.7 - Prob. 151FEPCh. 17.7 - Prob. 152FEPCh. 17.7 - Consider gas flow through a convergingdiverging...Ch. 17.7 - Combustion gases with k = 1.33 enter a converging...
Knowledge Booster
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
    • SEE MORE QUESTIONS
    Recommended textbooks for you
  • Elements Of Electromagnetics
    Mechanical Engineering
    ISBN:9780190698614
    Author:Sadiku, Matthew N. O.
    Publisher:Oxford University Press
    Mechanics of Materials (10th Edition)
    Mechanical Engineering
    ISBN:9780134319650
    Author:Russell C. Hibbeler
    Publisher:PEARSON
    Thermodynamics: An Engineering Approach
    Mechanical Engineering
    ISBN:9781259822674
    Author:Yunus A. Cengel Dr., Michael A. Boles
    Publisher:McGraw-Hill Education
  • Control Systems Engineering
    Mechanical Engineering
    ISBN:9781118170519
    Author:Norman S. Nise
    Publisher:WILEY
    Mechanics of Materials (MindTap Course List)
    Mechanical Engineering
    ISBN:9781337093347
    Author:Barry J. Goodno, James M. Gere
    Publisher:Cengage Learning
    Engineering Mechanics: Statics
    Mechanical Engineering
    ISBN:9781118807330
    Author:James L. Meriam, L. G. Kraige, J. N. Bolton
    Publisher:WILEY
  • Elements Of Electromagnetics
    Mechanical Engineering
    ISBN:9780190698614
    Author:Sadiku, Matthew N. O.
    Publisher:Oxford University Press
    Mechanics of Materials (10th Edition)
    Mechanical Engineering
    ISBN:9780134319650
    Author:Russell C. Hibbeler
    Publisher:PEARSON
    Thermodynamics: An Engineering Approach
    Mechanical Engineering
    ISBN:9781259822674
    Author:Yunus A. Cengel Dr., Michael A. Boles
    Publisher:McGraw-Hill Education
    Control Systems Engineering
    Mechanical Engineering
    ISBN:9781118170519
    Author:Norman S. Nise
    Publisher:WILEY
    Mechanics of Materials (MindTap Course List)
    Mechanical Engineering
    ISBN:9781337093347
    Author:Barry J. Goodno, James M. Gere
    Publisher:Cengage Learning
    Engineering Mechanics: Statics
    Mechanical Engineering
    ISBN:9781118807330
    Author:James L. Meriam, L. G. Kraige, J. N. Bolton
    Publisher:WILEY
    Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License