Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 12, Problem 30P
Plot the percentage discrepancy between the density at the stagnation point and the density at a location where the Mach number is M, of a compressible flow, for Mach numbers ranging from 0.05 to 0.95. Find the Mach numbers at which the discrepancy is 1 percent, 5 percent, and 10 percent.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Rewrite dV/V in terms of only Mach number and γ for a steady, adiabatic flow. Showall steps of the derivation clearly.
γ = 1.4, R=287 J/kgK
Air flowing at 32 kPa, 240 K, and Ma1 = 3.6 is forced to undergo an expansion turn of 15°. Determine the Mach number, pressure, and temperature of air after the expansion.
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.
Chapter 12 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 12 - Air is expanded in a steady flow process through a...Ch. 12 - Five kilograms of air is cooled in a closed tank...Ch. 12 - Air is contained in a piston-cylinder device. The...Ch. 12 - Calculate the power delivered by the turbine per...Ch. 12 - If hydrogen flows as a perfect gas without...Ch. 12 - A 1-m3 tank contains air at 0.1 MPa absolute and...Ch. 12 - Air enters a turbine in steady flow at 0.5 kg/s...Ch. 12 - Natural gas, with the thermodynamic properties of...Ch. 12 - Carbon dioxide flows at a speed of 10 m/s in a...Ch. 12 - In an isothermal process, 0.1 cubic feet of...
Ch. 12 - Calculate the speed of sound at 20C for (a)...Ch. 12 - An airplane flies at 550 km/hr at 1500 m altitude...Ch. 12 - Actual performance characteristics of the Lockheed...Ch. 12 - For a speed of sound in steel of 4300 m/s,...Ch. 12 - Determine and plot the Mach number of an...Ch. 12 - Investigate the effect of altitude on Mach number...Ch. 12 - The grandstand at the Kennedy Space Center is...Ch. 12 - Use data for specific volume to calculate and plot...Ch. 12 - An object traveling in atmospheric air emits two...Ch. 12 - An object traveling in atmospheric air emits two...Ch. 12 - While at the seashore, you observe an airplane...Ch. 12 - The temperature varies linearly from sea level to...Ch. 12 - Prob. 23PCh. 12 - A photograph of a bullet shows a Mach angle of 32....Ch. 12 - An F-4 aircraft makes a high-speed pass over an...Ch. 12 - All aircraft passes overhead at 3 km altitude. The...Ch. 12 - A supersonic aircraft flies at 3 km altitude at a...Ch. 12 - For the conditions of Problem 12.27, find the...Ch. 12 - The Concorde supersonic transport cruised at M =...Ch. 12 - Plot the percentage discrepancy between the...Ch. 12 - Compute the air density in the undisturbed air and...Ch. 12 - Carbon dioxide flows in a duct at a velocity of 90...Ch. 12 - If nitrogen at 15C is flowing and the stagnation...Ch. 12 - An aircraft cruises at M = 0.65 at 10 km altitude...Ch. 12 - High-speed aircraft use air data computers to...Ch. 12 - A supersonic wind tunnel test section is designed...Ch. 12 - Oxygen flows in a passage at a pressure of 25...Ch. 12 - What is the pressure on the nose of a bullet...Ch. 12 - Prob. 39PCh. 12 - Air flows in an insulated duct. At point the...Ch. 12 - Consider steady, adiabatic flow of air through a...Ch. 12 - Air passes through a normal shock in a supersonic...Ch. 12 - A Boeing 747 cruises at M = 0:87 at an altitude of...Ch. 12 - Space debris impact is a real concern for...Ch. 12 - A CO2 cartridge is used to propel a toy rocket....Ch. 12 - Nitrogen flows from a large tank, through a...Ch. 12 - Air flows from the atmosphere into an evacuated...Ch. 12 - Oxygen discharges from a tank through a convergent...Ch. 12 - The hot gas stream at the turbine inlet of a JT9-D...Ch. 12 - Carbon dioxide discharges from a tank through a...Ch. 12 - Air at 100F and 100 psia in a large tank flows...Ch. 12 - Calculate the required diameter of a convergent...Ch. 12 - Steam flows steadily and isentropically through a...Ch. 12 - Nitrogen flows through a diverging section of duct...Ch. 12 - At a section in a passage, the pressure is 30...Ch. 12 - In a given duct flow M = 2.0; the velocity...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Five pounds of air per second discharge from a...Ch. 12 - Air flows isentropically through a...Ch. 12 - Air, at an absolute pressure of 60.0 kPa and 27C,...Ch. 12 - Carbon dioxide flows from a tank through a...Ch. 12 - A convergent-divergent nozzle of 50-mm tip...Ch. 12 - Air flows adiabatically through a duct. At the...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Atmospheric air at 98.5 kPa and 20C is drawn into...Ch. 12 - The exit section of a convergent-divergent nozzle...Ch. 12 - Air flowing isentropically through a converging...Ch. 12 - Air flows from a large tank at p = 650 kPa...Ch. 12 - A converging nozzle is connected to a large tank...Ch. 12 - Air at 0C is contained in a large tank on the...Ch. 12 - A large tank initially is evacuated to 10 kPa...Ch. 12 - Air flows isentropically through a converging...Ch. 12 - Air enters a converging-diverging nozzle at 2 MPa...Ch. 12 - Prob. 75PCh. 12 - A jet transport aircraft, with pressurized cabin,...Ch. 12 - A converging-diverging nozzle, with a throat area...Ch. 12 - Air, at a stagnation pressure of 7.20 MPa absolute...Ch. 12 - A small rocket motor, fueled with hydrogen and...Ch. 12 - Testing of a demolition explosion is to be...Ch. 12 - A total-pressure probe is placed in a supersonic...Ch. 12 - Air flows steadily through a long, insulated...Ch. 12 - Air discharges through a convergent-divergent...Ch. 12 - A normal shock wave exists in an airflow. The...Ch. 12 - Air approaches a normal shock at V1 = 900 m/s, p1...Ch. 12 - Air approaches a normal shock at M1 = 2.5, with...Ch. 12 - Air undergoes a normal shock. Upstream, T1 = 35C,...Ch. 12 - If, through a normal shock wave in air, the...Ch. 12 - The stagnation temperature in an airflow is 149C...Ch. 12 - A supersonic aircraft cruises at M = 2.2 at 12 km...Ch. 12 - The Concorde supersonic transport flew at M = 2.2...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
ICA 8-57
A 100-watt [W] motor (60% efficient) is available to raise a load 5 meters [m] into the air. If the ta...
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
Consider refrigerant R-134a flowing in a smooth, horizontal, tube of wall thickness 2 mm. The refrigerant is at...
Fundamentals of Heat and Mass Transfer
How much time will be required for a milling machine to face mill an AISI 1020 steel surface BHN 150, that is 1...
Degarmo's Materials And Processes In Manufacturing
Three rigid bodies, 2,3, and 4, are connected by four springs as shown in the figure. A horizontal force of 1,0...
Introduction To Finite Element Analysis And Design
A loading causes the block to deform into the dashed shape. Explain how to determine the strains (A) xy, (B)xy....
Mechanics of Materials (10th Edition)
The quantity ms into s.
Engineering Mechanics: Statics & Dynamics (14th Edition)
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
- Race cars at the Indianapolis Speedway average speeds of185 mi/h. After determining the altitude of Indianapolis,fi nd the Mach number of these cars and estimate whethercompressibility might affect their aerodynamics.arrow_forwardThe Mach number behind a normal shock wave is 0.4752. What is the Mach number in front of the wave? What are the density, pressure, and temperature ratios across the shock?arrow_forwardAn aircraft is flying at 440 km/hr at 3 km on a standard day. What is the aircraft Mach Number?arrow_forward
- Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.6. If the pressure and temperature of air are 58 kPa and 270 K, 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.arrow_forwardCan the Mach number of a fluid be greater than 1 after a normal shock wave? Explain.arrow_forward2. Determine the final Mach number and density in the compressive case with an initial Mach number of 1.75 and a deflection of 10° using the exact theory method. Assume normal sea-level conditions.arrow_forward
- In a wind tunnel air enters with a velocity of 200kmph. The static pressure and temperature of the air at the inlet of the tunnel is 110kPa and 27°C respectively. Determine Mach number, stagnation temperature, stagnation pressure and the stagnation density on a test model installed in the wind tunnel. The size of the tunnel is given as 1m x1m square cross-section. Determine the mass flow rate of the air. For air assume R=287J/kgK ; γ=1.4.arrow_forwardFind the expression 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 Ma1arrow_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_forward
- Calculate the ratio of kinetic energy to internal energy at a point in an airflow where the Mach number is: (a) M = 2, and (b) M = 20.arrow_forwardConsider air entering a heated duct at p1 = 1 atm and T1 = 288 K. Ignore the effect of friction. Calculate the amount of heat per unit mass (in joules per kilogram) necessary to choke the flow at the exit of the duct for an inlet Mach number of M1 = 2.2.arrow_forwardThe Mach number of an aircraft that travels with a speed of 260 m/s in air at 25° C while it undergoes the compressibility effect will be: (Use speed of sound in air at 0° C: 331 m/s) Select one: a. M = 0.69 b. M= 0.70 c. M= 0.75arrow_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 PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering 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