Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 10, Problem 10.9P
Consider a convergent-divergent nozzle with an exit-to-throat area ratio of 1.53. The reservoir pressure is 1 atm. Assuming isentropic flow, except for the possibility of a normal shock wave inside the nozzle, calculate the exit Mach number when the exit pressure
(a) 0.94 atm (b) O.886 atm (c) 0.75 atm (d) 0.154 atm
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
At some section in the convergent-divergent nozzle, in which air is flowing,
pressure, velocity, temperature and cross-sectional area are 200 kN/m², 170 m/s, 200°C and 1000
mm² respectively. If the flow conditions are isentropic, determine:
(i) Stagnation temperature and stagnation pressure, (ii) Sonic velocity and Mach number at this
section, (iii) Velocity, Mach number and flow area at outlet section where pressure is 110 kN/m²,
(iv) Pressure and temperature at throat of the nozzle. Take for air: R=287 J/kg K, cp = 1.0 kJ/kg
K and k = 1.4
For non-isentropic constant-area flow with stagnation temperature change the following
relation was determined:
Y
1
To _ ²(y + 1)M² (1 + ¹ Z ¹ M²)
2
TO
(1+yM²)²
It is possible to use the above equation and calculate the downstream Mach number without
resorting to iteration for a flow where the upstream Mach number, as well as the upstream
and downstream stagnation temperatures, are known. This is a common calculation for flows
through engine combustors.
Presuming the left side is a known quantity, show that the above equation can be directly
solved as a quadratic in M² and which roots correspond to the subsonic/supersonic solution.
Rewrite the equation as: aM4 + bM² + c = 0, and then M² = (−b ± √b² - 4ac)/2a.
Determine the appropriate expressions for a, b, and c.
A convergent-divergent
operating isentropically.
Pback
P01
= 0.8
3
nozzle has an exit Mach number of 1.8 when
If the back pressure is increased such that:
Show Transcribed Text
a shock appears in the divergent portion. What is
Aerit
Ashock
Chapter 10 Solutions
Fundamentals of Aerodynamics
Ch. 10 - The reservoir pressure and temperature for a...Ch. 10 - A flow is isentropically expanded to supersonic...Ch. 10 - A Pitot tube inserted at the exit of a supersonic...Ch. 10 - For the nozzle flow given in Problem 10.1, the...Ch. 10 - A closed-form expression for the mass flow through...Ch. 10 - Prob. 10.6PCh. 10 - A convergent-divergent nozzle with an...Ch. 10 - For the flow in Problem 10.7, calculate the mass...Ch. 10 - Consider a convergent-divergent nozzle with an...Ch. 10 - A 20 half-angle wedge is mounted at 0 angle of...
Ch. 10 - The nozzle of a supersonic wind tunnel has an...Ch. 10 - We wish to design a supersonic wind tunnel that...Ch. 10 - Consider a rocket engine burning hydrogen and...Ch. 10 - For supersonic and hypersonic wind tunnels, a...Ch. 10 - Return to Problem 9.18. where the average Mach...Ch. 10 - Return to Problem 9.19, where the average Mach...Ch. 10 - A horizontal flow initially at Mach I flows over a...Ch. 10 - Consider a centered expansion wave where M1=1.0...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
What types of coolant are used in vehicles?
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Locate the centroid of the area. Prob. 9-17
Engineering Mechanics: Statics
17–1C A high-speed aircraft is cruising in still air. How does the temperature of air at the nose of the aircra...
Thermodynamics: An Engineering Approach
The triple jump is a track-and-field event in which an athlete gets a running start and tries to leap as far as...
Vector Mechanics For Engineers
Steady state conduction rate to the warm compressor to the net power produces theoretically by thermodynamic ba...
Introduction to Heat Transfer
Describe the structural changes that take place when a plain-carbon eutectoid steel is slowly cooled from the a...
Foundations of Materials Science and Engineering
Knowledge Booster
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
- Asap.. An isentropic flow through a convergent-divergent nozzle with an exit-to-throat ratio of Ae/At = 2.2. The flow through the throat is subsonic and the exit pressure is pe = 0.967 atm. The inlet pressure is p = 1 atm. Determine the Mach number (Mt) at the Throat.arrow_forwardAir is flowing in a convergent nozzle. At a particular location within the nozzle the pressure is 280 kPa, the stream temperature is 345 K. and the velocity is 150 m/s. If the cross-sectional area at this location is 9.29 x 103 m², find: (a) The Mach number at this location, (b) The stagnation temperature and pressure. (c) The area, pressure, and temperature at the exit where M-1.0. (d) The mass rate of flow for the nozzle. Indicate any assumptions you may make and the source of data used in the solution.arrow_forward1. Air flow isentropically through a converging nozzle attached to a reservoir, where the pressure is 170 kPa and temperature is 300 K. At the inlet to the nozzle the Mach number is 0.2, the nozzle discharge to the atmosphere (100kPa). The discharge area is 0.02 m?. Determine the magnitude and direction of the force that must be applied to hold the nozzle in place.arrow_forward
- flow angle is measured as 15.8°. Assuming the flow is isentropic, determine the e per unit frontal area, the exit Mach number and the static pressure ratio acrossarrow_forwardMach number at a certain section in a diverging part of a c-d nozzle is 0.7. At farther section (towards the exit), Mach number reduces to 0.4. Hence, the cross-sectional area of the farther section is greater byarrow_forwardAir enters a 5-cm-diameter duct at Mach number = 0.2, a temperature of 550 K and a pressure of 200 kPa. The average friction factor for the duct is 0.016. If the Mach number at the duct exit is 0.8, determine the pressure at the duct exit. (For air constant R = 287 J/kg.K, specific heat ratio K = 1.4). Select one: a. 65.95 kPa b. 54.85 kPa c. 80.75 kPa d. 47.27 kPaarrow_forward
- The normal shock wave moves toward the back tank at an underexpansion flow regime during the operation of the converging-diverging nozzle True Or false??arrow_forwardConsider the isentropic flow through a convergent-divergent nozzle with an exit-to-throat area ratio of 2.5. The reservoir pressure and temperature are 1 atm and 288 K, respectively. Calculate the Mach number, pressure, and temperature at both the throat and the exit for the cases where (a) the flow is supersonic at the exit and (b) the flow is subsonic throughout the entire nozzle except at the throat, where M = 1.arrow_forward3. Consider a normal shock wave in a supersonic airstream where the pressure upstream of the shock is 1 atm. Calculate the loss of total pressure across the shock wave when the upstream Mach number is (a) M1 2.8, and (b) M1 = 4.4. Compare these two results and comment on their implication.arrow_forward
- Heat is rejected from the air flowing in a constant area duct. At the duct entrance, the air is moving at 200 m/s and possesses static conditions of 300 K and 100 kPa. If 50000 J/kg is rejected along the duct, find the exit Mach number, stagnation temperature change and the stagnation pressure change. [Ans. M2 = 0.48, To1 – To2 = 49.75 K, p02 – poi 13.02 kPa]arrow_forwardQ.2. Air flows through a constant-area duct is connected to a reservoir at a temperature of 500°C and a pressure of 500 kPa by a converging nozzle, as shown in Figure. Heat is lost at the rate of 250 kJ kg. Determine the exit pressure and Mach number and the mass flow rate for a back pressure of 0 kPa. q- 250 kJkg P = 500 kPa T,= 500°C Ps = 0 kPa D=0.02marrow_forward1)Air is supplied to a converging nozzle from a large reservoir where the temperature and pressure are 400 Kand 150 kPa, respectively. At a certain cross-section where the area Is 0.01 m2, the pressure and velocity are 100 kPa and 120 ms·', respectively. Assuming adiabatic flow, find the Mach number at this cross-section and determine the mass flow rate. 2) Helium flows adiabatically through a duct. At some section, where the area is 0.02 m2, the velocity is 500 ms·1 and the pressure is 100 kPa. Find the Mach number at the given section, and determine the mass flow rate if the stagnation temperature is 300 Karrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher: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