Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 3, Problem 3.16P
Consider the nonlifting flow over a circular cylinder of a given radius, where
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(a) A wing section with a chord of c and a span of b is mounted at
zero angle of attack in a wind tunnel. A pitot probe is used to
measure the velocity profile in the viscous region downstream of the
wing section as shown in the figure. The measured velocity profile
is u(z) = U∞ - (U/2) cos[TZ/(2w)] for -w ≤ z ≤w. Here, w =
0.02c. Assuming a constant pressure p = po along the streamlines
(dashed lines in the figure) and across the wake where the velocity
was measured, calculate the friction drag coefficient Cp, of the wing
section.
U
Streamlines
u = U_ -- cos 22
2W²
+w
Viscous wake
=
-W
(b) Consider a thin flat plate at zero angle of attack in an airflow at
P∞ =
1.225 kg/m³, T∞ = 288 K and μ∞ 1.7894 x 10-5 kg/m/s.
The length of the plate is 2 m and the span is 0.5 m. Assume the
boundary layers on the plate are laminar throughout (on the upper
and lower surfaces both) where LBL(x)/x = 0.664/√√/Rex applies.
The freestream velocity is 100 m/s. Calculate the friction drag (Df)
of the first…
The two-dimensional incompressible flow-field around a Rankine vortex of strength r and core size R,
has only a circumferential component, v. The value of v is given as follows:
R
г
v(r)
Tr
r R
2r
Determine the vorticity of this flow-field and the pressure coefficient, Cp, and plot them as a function of
r/R. The non-dimensional pressure coefficient C, is defined below. Where is the pressure expected to
be minimum, and what is the value of the minimum C,? (Use polar coordinates)
p - Poo
Cp
where p. is the pressure at infinity, and p is the density of the fluid. VR is the flow velocity at the outer
edge of the vortex core (i.e. at r= R)
(a)
Use the y-momentum equation to show that the pressure
gradient across the boundary layer is approximately zero i.e.
= 0 . Assume the boundary layer to be a two-dimensional
ду
steady and incompressible flow. Neglect gravitational
forces. State clearly all assumptions made.
Use the Bernoulli's equation to prove that the pressure
difference is given by
(b)
P2-P1 = -4pU?
for a fluid with constant density p flowing from point 1 to
point 2 where pi, U1, A1 are the pressure, velocity and flow
cross-section area at point 1 and p2, U2, A2 are the pressure,
velocity and flow cross-section area at point 2 respectively.
The ratio of the cross-section area
A1
= 3.
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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