Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 11, Problem 11.3P
Under low-speed incompressible flow conditions, the pressure coefficient at a given point on an airfoil is
a. The Prandtl-Glauert rule
b. The Karman-Tsien rule
c. Laitone’s rule
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Students have asked these similar questions
A Pitot tube is inserted into an airflow where the static pressure is 1 atm. Calculate the flow Mach number when the Pitot tube measures (a) 1.276 atm, (b) 2.714 atm, (c) 12.06 atm.
(a) A pitot tube indicates a pressure of 265 kPa in an airstream in which the temperature is 10°C
and the local Mach number is 1.5. Find the static pressure in the airstream.
(b) In another problem, a normal shock wave occurs in air at a point where the stagnation
temperature is 300°C and the velocity is 700 m/s. The stagnation pressure is 700 kPa. Under this
situation do the following:
(i) Draw a diagram and label all flow conditions.
(ii) Evaluate the Mach numbers, static and stagnation pressures, static and stagnation temperatures
before and after the normal shock. Give reasons to justify your answers.
Example 2. A high-speed AC 130 gunship is flying at a pressure altitude of 10 km. A
Pitot tube on the wingtip measures a pressure of 4.24 x 10ª N/m2. Calculate the
Mach number at which the aircraft is flying.
Solution: Solving for P1 at an altitude of 10000 m, we get 2.65 x 104 N/m2
k-1
1.4-1
Po
k
4.24 x 104)
1.4
M?
k – 1
- 1
- 1
1.4 – 1
2.65 x 104
M? = 0.719
M1 = 0.848
Chapter 11 Solutions
Fundamentals of Aerodynamics
Ch. 11 - Consider a subsonic compressible flow in cartesian...Ch. 11 - Using the Prandtl-Glauert rule, calculate the lift...Ch. 11 - Under low-speed incompressible flow conditions,...Ch. 11 - In low-speed incompressible flow, the peak...Ch. 11 - For a given airfoil, the critical Mach number is...Ch. 11 - Consider an airfoil in a Mach 0.5 freestream. At a...Ch. 11 - Prob. 11.7PCh. 11 - Consider the flow over a circular cylinder; the...Ch. 11 - In Problem 11.8, the critical Mach number for a...
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- An aircraft is flying at supersonic speed. At a component of an aircraft where the flow is perpendicular, the density ratio is 5. Solve for: a.Mach Number Downstream b. Pressure Ratio c. Temperature Ratio d. Mach Number upstreamarrow_forward5. At 30000ft, estimate the magnitude of transonic drag rise. Using this estimate, calculate the maximum velocity of the airplane at this altitude. Assume drag-divergence Mach number of 0.82 and d(D/D₁)/dM = 14.3 where D₁=1750lb is drag at Mach number 0.9 and D₂ = 4250lb at Mach number 1. 6 Estimate maximum range at 30000€ Also calculate the flight speed to obtain thisarrow_forwardAn aircraft is flying at supersonic speed. At a component of an aircraft where the flow is perpendicular (normalshock), the density ratio is 5. Solve for: a.Mach Number Downstream b. Pressure Ratio c. Temperature Ratio d. Mach Number upstreamarrow_forward
- The Mach no. of a fixed geometry inlet at overspeeded for starting mode (Ai= 0.13 m2, ,At= 0.095 m2) 0.41 O 2.77 O 1.72 O 0.49 Oarrow_forwardProblem 5. A Boeing 747 cruises at a Mach number of Ma = 0.87 at an altitude of z = 13 km on a standard day. A window in the cockpit is located where the external flow outside the window is at a Mach number of Ma = 0.2 relative to the plane surface (just outside the boundary layer). The cabin is pressurized to an equivalent altitude of z = 2.5 km for a standard atmosphere. (a) Estimate the pressure difference across the window and specify the direction of the net pressure force. (b) Sketch the stagnation pressure, static pressures, and critical pressure on a T-s diagram.arrow_forwardQ2: Air (y = 1.4) enters a converging-diverging diffuser with a Mach number of 2.8, static pressure pi of 100 kPa, and a static temperature of 20°C. For the flow situation shown in Figure, find the exit velocity, exit static pressure, and exit stagnation pressure. Ans: Ve = 55.093 m/s; Pe = 2236.678 kPa; Poe = 2252.44 kPa i M₁ = 2.8 A₁ = 0.10 m² A₂ = 0.50 m² A₁ = 0.25 m²arrow_forward
- -.2. A perfect gas (y = 1.4) enters a converging-diverging nozzle with a Mach number of 0.50 and local pressure and temperature values of 280 kPa and 280 K, respectively. The nozzle throat area is 6.5 X 10-4 m? and the nozzle exit area is 26 X 10-4 m². The nozzle exit pressure is 170 kPa. (a) What are the values of the Mach number and the stream temperature at the exit? (b) At what area does the shock occur? Show your method of solution on a skeleton flow chart.arrow_forwardQ6: Air following through constant area duct encounters stationary shock as shown in figure. Find the Mach number, temperature, pressure, stagnation pressure, stagnation temperature and velocity after the shock. Ans.: M2 = 0.6746, T2 = 344 K, p2 = 137 kPa, To = 375 K, po = 186 kPa. V1=500 m/s P;=50 kPa 1-250 K → (1) | (2)arrow_forward4.2 Test results obtained on a NACA 23012 airfoil show the following data: aº C₁ 0 0.15 9 1.20 If this airfoil is used in the design of an elliptical wing with aspect ratio, A=7.0, determine the wing lift curve slope at low Mach numbers.arrow_forward
- For a converging-diverging nozzle that is choked what is the ratio of nozzle area divided by the throat area for a Mach number of 2.1? (Assume isentropic flow for an ideal gas and k = 1.4.) Enter your answer to the fourth decimal place.arrow_forwardFor Air Assume: y =1.4 and R = 287 J/kg K Question B1 a) Air is flowing at a Mach number of 0.6 in a two-dimensional duct at a location where the area is of 0.75 m². At this location the static pressure is 50 kPa and the static temperature is 300 K. 1- Calculate the mass flow rate through the duct; [2 marks] 2- What percentage in area change would be necessary to reach a Mach number of 0.75? [2 marks] 3- What percentage in area change would be necessary to reach a Mach number of 1.00? [2 marks] b) A normal shock wave occurs in a gas with an unknown specific heat ratio. The static pressure ratio across the normal shock wave is 10.6. The Mach number downstream of the shock wave is equal to 0.495, find the specific heat ratio of the gas and the velocity ratio across the shock wave. [8 marks] c) Explain why successive infinitesimal compression waves tend to reinforce and form a shock wave. Use sketches to illustrate your answer. [5 marks] d) Show that for a choked convergent nozzle further…arrow_forwardb) In a converging-diverging duct the flow conditions are such that a normal shock is formed at the exit of the diverging section. Upstream of the shock the flow conditions are as below. Mach number= '5.198', Pressure= '311886.9' Pa and Temperature= '228.72' K. Obtain the Mach number, pressure, and temperature at the downstream of the shock. Assume standard air properties (y=1.4).arrow_forward
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