Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 9.3P
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Q1) Air at mach number 2 , pressure 0.5* 10° N/m² and a temperature of 0 °C ,
over a wedge and generation of an oblique shock wave 40° . determine :
1. Static pressure and temperature downstream the shock.
2. The mach number of the flow downstream the shock.
3. The wedge angle.
***********
Q2) As shown in figure (1) A mach number 2.4 air stream at oblique shock angle of
(B1-2 =30°) of incident shock with turning angle (0=10°). determine :
1. the mach number of the flow upstream the reflected shock.
2. the mach number of the flow downstream the reflected shock.
M2
M3
Figure (1)
At a point in the flow over an F-15 high-performance fighter airplane, the density,temperature and Mach number are 1 kg/m3, 240 Kelvin, and Mach 1.6.(a) At this point, calculate T0, ρ0, p0, a0, T ∗, a∗, p∗ and the flow velocity.(b) Calculate M ∗1 and, using the Prandtl relation, calculate M ∗2 and u2 after a normalshock.
4. It is important to remember that the isentropic relations and normal shock relationsare monotonic with Mach number and can be inverted. To illustrate this, consider thefollowing problems,
(c) If the temperature jumps from 0 Celsius ahead of a shock to 200 Celsius behinda shock, what is the shock Mach number?(d) If the velocity behind a Mach 5 shock wave is 200 m/s, what is the upstreamvelocity?
Chapter 9 Solutions
Fundamentals of Aerodynamics
Ch. 9 - A slender missile is flying at Mach 1.5 at low...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Equation (8.80) does not hold for an oblique shock...Ch. 9 - Consider an oblique shock wave with a wave angle...Ch. 9 - Consider the flow over a 22.2 half-angle wedge. If...Ch. 9 - Consider a flat plate at an angle of attack a to a...Ch. 9 - A 30.2 half-angle wedge is inserted into a...Ch. 9 - Consider a Mach 4 airflow at a pressure of 1 atm....Ch. 9 - Consider an oblique shock generated at a...Ch. 9 - Consider the supersonic flow over an expansion...
Ch. 9 - A supersonic flow at M1=1.58 and p1=1atm expands...Ch. 9 - A supersonic flow at M1=3,T1=285K, and p1=1atm is...Ch. 9 - Consider an infinitely thin flat plate at an angle...Ch. 9 - Consider a diamond-wedge airfoil such as shown in...Ch. 9 - Consider sonic flow. Calculate the maximum...Ch. 9 - Consider a circular cylinder (oriented with its...Ch. 9 - Consider the supersonic flow over a flat plate at...Ch. 9 - (The purpose of this problem is to calculate a...Ch. 9 - Repeat Problem 9.18, except with =30. Again, we...Ch. 9 - Consider a Mach 3 flow at 1 atm pressure initially...Ch. 9 - The purpose of this problem is to explain what...
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- = 1.2 bar, and M1 = 3.0. An 2- Conditions before a shock are T1 = 40°C, pl oblique shock is observed at 45° to the approaching air flow. (a) Determine the Mach number and flow direction after the shock. (b) What are the temperature and pressure after the shock?arrow_forwardQ4/ Air enters a duct with a Mach number of 2.0, and the temperature and pressure are 170 K and 0.7 bar, respectively. Heat transfer takes place while the flow proceeds down the duct. A converging section (A2/A3 = 1.45) is attached to the outlet as shown in Fig. Q4, and the exit Mach number is 1.0. Assume that the inlet conditions and exit Mach number remain fixed. Find the amount and direction of heat transfer in the duct: (a) If there are no shocks in the system. (b) If there is a normal shock someplace in the duct. M, - 2.0 T,- 170 K P-0.7 bar M, = 1.0 Fig.Q4 AzlA, = 1.45arrow_forwardQ.28 Superheated steam at 1500 kPa, has a specific volume of 2.75 m³/kmol and compressibility factor (Z) of 0.95. The temperature of steam is integer] (a) 249 (c) 522 °C [Round off to the nearest (b) 471 (d) 198arrow_forward
- Compressible Flow and Propulsion 1. Determine the speed of sound in Argon at 120 °C. Molecular weight of Argon = 40 kg/kmol and y= 1.667. (Ro = 8314.5 J/kmol K) %3D [Ans. 369 m/s] 2. Calculate the Mach number corresponding to the following speeds at an am temperature of 15 °C. Rair = 287 J kg*K, 1 mph = 0.447 ms?. ent (a) National speed limit of 70 mph [Ans. 0.09] (b) A top speed of 230 mph attained by a Formula driver. [Ans. 0.3] 3. Calculate the speed of an aircraft cruising in 20°C air where the angle of the zone of silence is a. 10° to the direction of travel. [1946ms) b. 20° to the direction of travel. [943ms] c. 80° to the direction of travel. [60ms] d. What is the maximum expected angle for M = 1? 4. Calculate the speed of sound during the flight of an aircraft for the two conditions (a) when it is at a cruising altitude of 10,000 m and the outside temperature is-60 °C. (b) when it lands in a desert city at a temperature of 45 °C (c) If the Mach number during cruising condition…arrow_forwarddetermine the Mach number, total pressure, and total temperature after the heat interaction for the following gases: a) y= 1.4 and cp 0.24 Btu/(lbm- °R) b) y= 1.325 and cp = 0.28 Btu/(1bm · °R) %3Darrow_forwardWhat is the Mach number of an airflow with a velocity of 2000m/s, at 2,000 ft altitude?arrow_forward
- For given air flow with Mach number in test section (i.e. at CD nozzle exit), Me = 8, T01 = 300 K, pressure in test section = 4000 Pa. (1) What is the value of static temperature, stagnation temperature and stagnation pressure in the test section? (2) What is the value of stagnation pressure in the storage thank? (3) What do you conclude about state of air? (4) What is the solution to rectify this problem. i.e. (5)What is the minimum temperature of air should you take in reservoir tank? At this condition, what is mass flow rate in test section? Low pressure air chamber High pressure air storage Storage tank T01 = 300K P01 = ? Settling chamber Pressure regulator Nozzle Screens Test-section Pe = 4000 Pa Me = 8 Te = ? K Sonic throat P0e =? T0e = ? Blow down wind Tunnel (Open circuit type) Diffuser Second throat vacuum tankarrow_forwardA near-ideal gas has a molecular weight of 44 and a specific heat c v =610 J/(kg ∙ K). What are ( a ) its specific heatratio, k , and ( b ) its speed of sound at 100 ° C?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
- The mass flow rate of a calorically perfect gas (C₁ = constant) through a Convergent-Divergent nozzle is given by, m = A Pt VT₁ M (1+ y +1 YM²) 2(3-1) (a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T₁ is total temperature, M is Mach number, A is local area of nozzle. (b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and obtain below relation. m A Pt √√Tt Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow. Hint: https://www.grc.nasa.gov/www/k-12/rocket/mflchk.html y+1 2(y-1) √(4¹) Rarrow_forwardA normal shock occurs in a stream of oxygen. The oxygen flows at Ma=1.8 and the upstream pressure and temperature are 40 psia and 85 degrees Fahrenheit. a) Calculate the following on the downstream side of the shock: static pressure, stagnation pressure, static temperature, stagnation temperature, static density, and velocity. b)If the Mach number is doubled to 3.6, what will be the resulting values of the parameters listed in part (a)?arrow_forwardThe propagation of disturbances from a point source that results in an oblique shock wave can be visualized in Figure Q2(b). From the diagram, derive the equation that relates Mach angle with the local Mach number.arrow_forward
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