FUND OF AERODYNAMICS(LLF) +CONNECT (1YR)
6th Edition
ISBN: 9781265141387
Author: Anderson
Publisher: MCG
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Chapter 10, Problem 10.16P
Return to Problem 9.19, where the average Mach number across the two-dimensional flow in a duct was calculated, and where
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An air tank with a nozzle, has a pressure of twice the standard sea level pressure and
density of 2.45 kg/m³. Outside the converging-diverging nozzle, the pressure corresponds
to an altitude of 3km and designed to have a mach number of 1.0 and 1.8 at the throat
and exit, respectively. The area at the throat is 0.15 square meters.
Calculate:
a) the temperature and speed of sound in the tank.
b) pressure and density at the throat
c) mass flow rate at the exit.
The Mach no. of a fixed geometry inlet at overspeeded for starting mode (Ai= 0.13 m2, At= 0.095 m2
For 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…
Chapter 10 Solutions
FUND OF AERODYNAMICS(LLF) +CONNECT (1YR)
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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- An impact tube is used to measure the Mach number of a certain airflowin a wind tunnel. The static pressure is 3 psia, and the impact pressure at theprobe is 116 kPa. What is the Mach number of the flow (k = 1.4 for air)? If thefree-stream air temperature is −40 ◦C, what is the flow velocity?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_forwardUnder low-speed incompressible flow conditions, the pressure coefficientat a given point on an airfoil is −0.54. Calculate Cp at this point when thefreestream Mach number is 0.58, usinga. The Prandtl-Glauert ruleb. The Karman-Tsien rulec. Laitone’s rulearrow_forward
- QUESTION 2 A compressor blade design tested in a cascade is found to choke with an inlet Mach number of 0.9 when the inlet flow angle is 52 deg. If the ratio of the throat area to the frontal area, A*/H1s, for the cascade is).625, calculate the loss of stagnation pressure between the far upstream and the throat and express this as a loss coefficient. Give your comments on what could cause this loss.arrow_forward02: The large compressed-air tank shown in the figure bellow exhausts from a nozzle at an exit velocity of V= 235 m/s. Assuming isentropic flow, compute: a) the exit Mach number. b) the pressure in the tank. (take; k = 1.396, C, = 917 J/Kg.k and R = 260 J/Kg.k) air at 30 "C tank conditions remain constant P- 101 kPaarrow_forwardA 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.arrow_forward
- The large compressed - air tank shown in the figure bellow exhausts from a nozzle at an exit velocity of Ve = 235 m / s. Assuming isentropic flow, compute: a) the exit Mach number. b) the pressure in the tank. (take; k = 1.396, Cp = 917 J / Kg.k and R = 260 J / Kg.k) air at 30 ° C tank conditions remain constant Pate = 101 kPaarrow_forward6.6. Air flows through a 0.25 m diameter duct. At the inlet the velocity is 300 m/s, and the stagnation temperature is 360 K. If the Mach number at the exit is 0.3, determine the direction and the rate of heat transfer. With the same conditions at the inlet, determine the amount of heat that must be transferred to the system if the flow is sonic at the exit.arrow_forwardExample 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 = 0.848arrow_forward
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