Fundamentals of Aerodynamics
Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
bartleby

Videos

Textbook Question
Book Icon
Chapter 11, Problem 11.1P

Consider a subsonic compressible flow in cartesian coordinates where the velocity potential is given by ϕ ( x , y ) = V x + 70 sin ( 2 π x ) 1 M 2 e 2 π y 1 M 2

If the freestream properties are given by V = 700 ft/s , p = 1 atm , and T = 519 ° R , calculate the following properties at the location ( x , y ) = ( 0.2 ft , 0.2 ft ) : M , p , and T.

Expert Solution & Answer
Check Mark
To determine

The Mach number of the subsonic compressible flow.

The temperature of the subsonic compressible flow.

The pressure of the subsonic compressible flow.

Answer to Problem 11.1P

The Mach number for the fluid at the given point is M=0.7067 .

The pressure for the fluid at the given point is p=0.933atm .

The temperature for the fluid at the given point is T=508.93°R .

Explanation of Solution

Given:

The freestream velocity of the compressible flow is V=700ft/s .

The pressure of the compressible flow is p=1atm .

The temperature of the compressible flow is T=519°R .

Formula used:

The velocity component in the x-direction is given as,

  u=ϕx

The velocity component in the y-direction is given as,

  v=ϕy

The expression for the Mach number is given as,

  M=VγRT

Here, γ is the ratio of specific heat, R is the specific gas constant and V is velocity of the flow.

The velocity of the flow is given as,

  V=u2+v2

The expression for the temperature for the given point is given as,

  CPT0=CPT+V22

The expression for the pressure is given as,

  p0p=(1+ γ1γM2)γγ1

Calculation:

The “Properties of air” is given as,

  γ=1.4R=1716ftlb/slug°RCP=6006ftlb/slug°R

The velocity component of the fluid in x-direction can be calculated as,

  u=ϕxu( 0.2ft,0.2ft)=(Vx+ 70sin( 2πx ) 1 M 2 e 2πy 1 m 2 xu=765.55ft/s

The velocity component of the fluid in the y-direction can be calculated as,

  v=ϕyv( 0.2ft,0.2ft)=(Vx+ 70sin( 2πx ) 1 M 2 e 2πy 1 m 2 xv=157.23ft/s

The resultant velocity of the flow can be calculated as,

  V=u2+v2V= ( 765.55 ft/s )2+ ( 157.23 ft/s )2V=781.53ft/s

The Mach number of the supersonic flow can be calculated as,

  M=V γR T M=700ft/s 1.4×1716 ftlb/ slug°R ×519°RM=0.6268

For M=0.6268 , the temperature at start can be calculated as,

  T0T=1+γ12M2T0519°R=1+1.412(0.6268)2T0=559.78°R

The pressure at starts can be calculated as,

  p0p=(1+ γ1 2 M 2)γ γ1p01atm=(1+ 1.41 2× 0.6268 2) 1.4 1.41p0=1.303atm

The required temperature can be calculated by the energy equation as,

  CPT0=CPT+V22T=T0V22CPT=559.78°R ( 781.53 ft/s )22×6006ftlb/slug°RT=508.93°R

The required Mach number can be calculated as,

  M=V γRTM=781.53ft/s 1.4×1716 ftlb/ slug°R ×508.93°RM=0.7067

The required pressure for the flow can be calculated as,

  p0p=(1+ γ1 2 M 2)γ γ11.303atmp=(1+ 1.41 2× ( 0.7067 ) 2) 1.4 1.41p=0.933atm

Conclusion:

Therefore, the Mach number for the fluid at the given point is M=0.7067 .

Therefore, the pressure for the fluid at the given point is p=0.933atm .

Therefore, the temperature for the fluid at the given point is T=508.93°R .

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
3-55 A multifluid container is connected to a U-tube, as shown in Fig. P3–55. For the given specific gravities and fluid column heights, determine the gage pressure at A. Also determine the height of a mercury column that would create the same pressure at A. Answers: 0.415 kPa, 0.311 cm
I need help answering parts a and b
Required information Water initially at 200 kPa and 300°C is contained in a piston-cylinder device fitted with stops. The water is allowed to cool at constant pressure until it exists as a saturated vapor and the piston rests on the stops. Then the water continues to cool until the pressure is 100 kPa. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Water 200 kPa 300°C On the T-V diagram, sketch, with respect to the saturation lines, the process curves passing through the initial, intermediate, and final states of the water. Label the T, P, and V values for end states on the process curves. Please upload your response/solution by using the controls provided below.

Additional Engineering Textbook Solutions

Find more solutions based on key concepts
Knowledge Booster
Background pattern image
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
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license