Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.14P
For supersonic and hypersonic wind tunnels, a diffuser efficiency,
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1. Air is flowing isentropically through a
converging duct which is fed from a large
reservoir where the temperature and
250 kPa,
pressure
are
350 K and
respectively. At a certain point along the
duct, where the cross-sectional area is
0.005 m, the pressure
is 150 kPa.
Determine the Mach number, temperature
and velocity at that point and also calculate
the mass flow rate. (Ans: 330.1 K, 0.549,
162.8 kPa, 1.718 kg-s").
2. Air is supplied to a converging nozzle from a
large reservoir where the temperature and
pressure are 400 K and 100 kPa, respectively.
At a certain cross-section, the temperature
and pressure are measured to be 383.8 K and
63 kPa, respectively. Assuming isentropic
flow, find the Mach number at this cross-
section and the mass flow rate per unit area.
(Ans: 0.46, 103.3 kg-s'-m²).
3. A converging nozzle is fed with air from a
large reservoir where the temperature and
pressure are 400 K and 170 kPa, respectively.
The nozzle has an exit…
A supersonic diffuser for air (y%3D1.4) has an arca ratio of 0.416 with an inlet Mach number
of 2.4 (design value). Determine the exit Mach number and the design value of the
pressure ratio across the diffuser for isentropic flow. At an off-design value of the inlet
Mach number (2.7) a normal shock occurs inside the diffuser. Determine the upstream
Mach number and area ratio at the section where the shock occurs and pressure ratio
across the diffuser.
The flow inside the intake of a scramjet is found to be supersonic with Mach number of 2.5. From the instrumentations located inside the intake section, the static pressure and temperature were measured as 1 atm and 290 K, respectively. Inside the intake, the flow encounters the first compression ramp at an angle of 22º. As an intake engineer, investigatethe flow properties (Mach number, static pressure and temperature, stagnation pressure and temperature) after the resulting first oblique shock wave, so that the 2ndcompression ramp can be designed according to the requirements. Use the relevant tables and charts to assist your investigation. Commentif more shock waves are required to ensure that subsonic combustion is possible.
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...
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- 3. 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_forwardA long pipe of 0.0254 m diameter has a mean coefficient of friction of 0.003. Air enters the pipe at a mach number of 2.5, stagnation temperature 310 K and static pressure 0.507 bar. Determine for a section at which the mach number reaches 1.2: i) Static pressure and temperature, ii) Stagnation pressure and temperature, iii) Velocity of air, iv) Distance of this section from the inlet and v) mass flow rate of air.arrow_forwardQ6- Air flows isentropically through converging-diverging nozzle. At a section where nozzle area is 0.0012 m², the local pressure, temperature and Mach number are 4.1 bars, 4.4 °C and 0.52 respectively. The back pressure is 2.06 bar. The Mach number at the throat, the mass flow rate, and the throat area are to be determined.arrow_forward
- The stagnation pressure and temperature at the entry of a nozzle are 5 bar and 500 K respectively. The exit Mach number is 2 where a normal shock wave occurs. Calculate the following quantities before and after the shock. Static and stagnation pressures and temperatures, air velocities and Mach numbers. What are the values of stagnation pressure loss and increase in entropy across the shock?arrow_forwardA perfect gas (gamma = 1.9) enters a converging-diverging nozzle with a Mach number of 0.98 and local pressure and temperature values of 490 kPa and 570 K, respectively. The nozzle throat area is 6.5 * 10^-4 m^2 and the nozzle exit area is 26*10^-4 m^2. The nozzle exit pressure is 170 КРа. Verify that the back pressure is such that a shock occurs. a) What are the values of the mach number and stream temperature at the exit? b) At what area does the shock occur?arrow_forwardQ.1. Air flow adiabatically in a constant area duct. At the inlet of the duct, the Mach number, pressure and temperature are 0.6, 150 kPa and 300 K respectively. Assuming a duct length of 0.45 m, a duct diameter of 0.03 m and a friction coefficient of 0.003, determine the Mach number, temperature, and pressure at the duct outlet. Also, calculate the mass flow rate.arrow_forward
- A supersonic nozzle is used for discharging air from a reservoir. The reservoir pressure and temperature are 0.5 MPa and 500 K. The design Mach number is 2. With back pressure, a normal shock appears at the exit of the nozzle. Determine the Mach number, pressure and temperature of air after the shock. [Ans. M2 = 0.577, p2 = 0.288 MPa, T, = 468.14 K] %3D ||arrow_forwardAir flows isentropically at a rate of 1.3 kg/s from a large chamber through a convergent- divergent duct and leave to the outlet at Mach number 2.72. The air velocity, pressure OUTM EXAMINATION SESSION 2020/2021 (a) Sketch the system and label all components with subsonic/supersonic and UTM N 2020/2021 TM FINAL EXAMIN 2020/2021 answer. 2020/2021 st TION STAL EXAMINATION SEMESTAR I, SESSJO , SESSIOVON 3, SERIONON Esto ON b/202 2020/202 and temperature at a location somewhere along the system were found to be 900 m/s, OUTM 150 kPa and 60°C, respectively. FINAL EXAMINATIC SEMESTER IL SESSION 2025/202 RATION 2020/2021 FINAL EXAMINA BEMENTER I SESSION 2020/202 diffuser/nozzle according to the effect of area change. Justify your ALE eSTER R, SESSION 202b/202 (b) Determine the pressure and temperature of the air in the large chamber, the area at throat, and the velocity at outlet. zb/202arrow_forwardThe pressure upstream of a normal shock wave is 1 atm. The pressure and temperature downstream of the wave are 10.33 atm and 1,390 °R, respectively. Calculate the Mach number and temperature upstream of the wave.arrow_forward
- 01: A convergent-divergent nozzle has an exit area to throat area ratio of 2. Air enters the nozzles with a stagnation pressure of 6.5 bar and a stagnation temperature of 93°C. The throat area is 6.25 cm. If there is a normal shock wave standing at a point where M= 1.5, determine the pressure, temperature on either side of the plane of shock and the mach number on the downstream side of the plane. Find also the exit mach number of the nozzle. M<1arrow_forward1. Air (y=1.4) enters a converging-diverging nozzle from a reservoir which is at a pressure of 300 kPa, and temperature 300 K. A normal shock occurs at a point where the area is 2 times the area of the throat. Find the pre and post shock Mach number, pressure, and temperature as well as the same values at the exit. Also, find exit values for a gas with y = 1.33 T, = 300 K Py = 300 kPa Agrot = 50 cm? Aşhock = 2 Athuoat 3 Aexit = 4 Aduoatarrow_forwardQ1- A converging nozzle with a throat area of 0.001² m is operated with air at aback pressure of 5.91 bars. The nozzle is fed from a large plenum chamber where the stagnation pressure and the temperature are 10 bars and 60 °C, respectively. The exit Mach number and mass flow rate are to be determined.arrow_forward
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