Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3.8P
Consider a uniform flow with velocity
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(30 minutes) Consider a converging-diverging nozzle, which is open to stagnant atmosphere
at the inlet and connected to an infinitely large low-pressure reservoir downstream at the
outlet (see the figure below). The ambient pressure (pa) is 1 bar, the throat cross section area
is 0.1 m². Imagine that the pressure in the low-pressure reservoir (p₁) can be changed to
regulate the flow in the nozzle.
Me
Pa=1 bar
A₁ =0.1 m²
Ae
Pv
Pe
Low pressure reservoir
a) It is known that when p₁
=
0.8 bar, the nozzle is choked and the flow in the converging-
diverging nozzle is subsonic. Find the exit cross-section area (Ae), the static pressure at
the exit (pe) and the Mach number at the exit (Me) for this case.
b) Determine the range of vacuum pressure (pv) for which there is a normal shock wave in
the diverging section of the nozzle.
c) Imagine that a pitot-tube is inserted at the exit of the nozzle. What would be the total
pressure reading when: (1) p₁ = 0.8 bar; (2) p, is adjusted such that the…
1. Five forces are applied to the solid prism shown in Figure 1.
Note that the 30 lb forces are in the plane of the prism's
surface and are not vertical. Also note that the end of the
prism is not an equilateral triangle.
a) Compute the magnitude of the couple moment of the
force couple formed by the 30 lb forces.
b) Replace all the forces with an equivalent resultant force
and couple moment acting at point A, Rand G. Give
your answers as Cartesian vectors.
Figure 1:
6 in
a) G
b) R
GA
B
5 in
5 in
4 in
40 lb
4 in
40 lb
A
50 lb
30 lb
5 in
E
5 in
Y
4) Calculate the thrust reduction due to the existence of a shock wave at the exit of the rocket no:
given below, compared to the no shock case.
P=200kPa
I
M=1.4
MCI
M = 1
T=mle
A₂ = 3m²
Chapter 3 Solutions
Fundamentals of Aerodynamics
Ch. 3 - For an irrotational flow. show that Bernoullis...Ch. 3 - Consider a venturi with a throat-to-inlet area...Ch. 3 - Consider a venturi with a small hole drilled in...Ch. 3 - Consider a low-speed open-circuit subsonic wind...Ch. 3 - Assume that a Pitot tube is inserted into the...Ch. 3 - A Pilot tube on an airplane flying at standard sea...Ch. 3 - At a given point on the surface of the wing of the...Ch. 3 - Consider a uniform flow with velocity V. Show that...Ch. 3 - Show that a source flow is a physically possible...Ch. 3 - Prove that the velocity potential and the stream...
Ch. 3 - Prove that the velocity potential and the stream...Ch. 3 - Consider the flow over a semi-infinite body as...Ch. 3 - Derive Equation (3.81). Hint: Make use of the...Ch. 3 - Derive the velocity potential for a doublet; that...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the nonlifting flow over a circular...Ch. 3 - Consider the lifting flow over a circular cylinder...Ch. 3 - The lift on a spinning circular cylinder in a...Ch. 3 - A typical World War I biplane fighter (such as the...Ch. 3 - The Kutta-Joukowski theorem, Equation (3.140), was...Ch. 3 - Consider the streamlines over a circular cylinder...Ch. 3 - Consider the flow field over a circular cylinder...Ch. 3 - Prove that the flow field specified in Example 2.1...
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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
- 3. (30 minutes) Find the mass flow rate for the converging-diverging nozzle below. A₁=0.1 m² V₁ = 150 m/s P₁ = 100 kPa T₁ = 20°C M>1arrow_forwardQ4. Derive the y-momentum equation for a thin laminar boundary layer using the general form of the y-momentum equation for two-dimensional and steady flow given below. до pu +pv- Əx до др მ dy ду +(x+7) ди дхarrow_forward1) Solve the problem using the superposition method. Check that your answer is correct.For steel, use a Poisson's ratio of 0.3.arrow_forward
- 3. Consider a subsonic compressible flow in Cartesian coordinates where the perturbation velocity potential is given by: 20 $(x,y) = -2π e 1-M sin(2x) √1 - M² The free-stream properties are Vo。 = 200 m/s, p∞ = 150 kPa and T∞ = 250 K. po a. Compute the Mach number at the location (x, y) = (0.8, 0.2). b. Compute the pressure coefficient at the wall at the wall at (x, y) = (0.8,0) using both the = 2 2û | and the small perturbation approximation (Cp = -2). exact relation [Cp = M-1)] andarrow_forwardQ2) (30 minutes) The pressure distribution over a curved surface is given below. Find an expression for the friction coefficient assuming there exists a turbulent boundary layer over the surface with a power law velocity profile as given in the figure. y P/Pmax 1.0 0.5- 0.25 - u = de y б → อ 0.3 1.0 ри 0 = PeUe de dx 8* = 1 - ри PeUe (1-0)ay 0 due -- Ue dx = dy 1 - Ue dy + น dy = (2 + H) = 1 Cf 2 - и Ue dy v2 + + gz = constant 2 Ρarrow_forwardQ3. A piecewise linear function approximates the velocity profile in an incompressible boundary layer flow over a flat plate, as shown in the figure below. Under the assumption of a constant edge velocity (U) in the streamwise direction (i.e., the x direction), calculate the skin friction coefficient as a function of the Reynolds number. وانه δ со 2/3 Ve Ve u 1- 8* = √² (1 - Du₂) dy pu ри PeUe น 9 = √²* Du (1-7) dy de dx 0 PeUe δ + 0 due (2+0²) = 12/24 Ue dx 8 ≤ 100arrow_forward
- 4. The streamwise velocity component (u) for a laminar boundary layer is given by: u = Ue 8 = b√√x where b is a constant and U is the edge velocity. Obtain an expression for the vertical velocity component (v) at the edge of the boundary layer.arrow_forwardPlease Solve Q1&Q2&Q3arrow_forwardFind the equations of motion of the double elastic pendulum below using Lagrange's equations.arrow_forward
- Problem 2. (35 pts) Consider the Atwood machine with rope length / depicted below. The spring with constant k is initially unstretched. Find the equations of motion using Lagrange multipliers by using the configuration coordinates y₁, y2, and y3. Y₁ m1 lllllllllllllllll k Уз Y2 m2arrow_forwardplz solve this ur selfarrow_forwardProblem 3. (30 pts) m m, m Consider the system of two homogeneous circular cylinders. Each of the cylinders has mass m and a moment of inertia, I=1/2mr2 around the center of mass, and rod AB has mass mr and length /. The cylinders have radius r and are assumed to roll without slipping. The system in on an incline and attached to wall by a spring of constant k at point A. The spring is initially unstretched. Find the equation(s) of motion by choosing generalized coordinate(s) and using Lagrange's equation(s).arrow_forward
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