Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 10, Problem 10.4P
For the nozzle flow given in Problem 10.1, the throat area is
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Q4. 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
дх
1) Solve the problem using the superposition method. Check that your answer is correct.For steel, use a Poisson's ratio of 0.3.
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)] and
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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- Q2) (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_forward4. 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_forward
- Please Solve Q1&Q2&Q3arrow_forwardFind the equations of motion of the double elastic pendulum below using Lagrange's equations.arrow_forwardProblem 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_forward
- plz 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_forwardCan you please Solve Q1 & Q2 &Q3arrow_forward
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