Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 2, Problem 2.7P
The velocity field given in Problem 2.3 is called source flow, which will be discussed in Chapter 3. For source flow, calculate:
a. The time rate of change of the volume of a fluid element per unit volume.
b. The vorticity.
Hint: It is simpler to convert the velocity components to polar coordinates and deal with a polar coordinate system.
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4. Consider steady flow of water through an axisymmetric garden hose nozzle (see Fig). Along the
center line of the nozzle, the water speed increases from uentrance to Uexit as sketched. Measurements
reveal that the centerline water speed increases parabolically through the nozzle. Write an equation
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Dentrance
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u(x)
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55. Derive the relation for angular velocity in terms of the velocity components
for fluid rotation in a two-dimensional flow field. [Hint: Use the schematic for ro-
tation in Figure IIa.3.5 and find the angular velocity for line oa as @a = doddt.
Substitute for da= dl,/dx and for dl, from dl, = (JV,/dx)dxdt. Do the same for line
ob to find @p. The z-component of rotation vector is the average of @a and @p.
Do the same for x- and y- components].
(a) A model low speed centrifugal compressor (a “blower") runs at 430 rpm and delivers 10 m/s
of air against a pressure head of 60 mm of water. If the pump efficiency is estimated to be 80%,
how much power is required to drive the compressor?
(b) A geometrically similar compressor is made with a diameter 1.8 times the size of the model
and is required to work against a pressure head of 80 mm of water. Determine the operating
speed and the power needed to drive the compressor assuming dynamically similar condi-
tions apply.
Chapter 2 Solutions
Fundamentals of Aerodynamics
Ch. 2 - Consider a body of arbitrary shape. If the...Ch. 2 - Consider an airfoil in a wind tunnel (i.e., a wing...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - Consider a velocity field where the radial and...Ch. 2 - Consider a velocity field where the x and y...Ch. 2 - The velocity field given in Problem 2.3 is called...Ch. 2 - The velocity field given in Problem 2.4 is called...Ch. 2 - Is the flow field given in Problem 2.5...Ch. 2 - Consider a flow field in polar coordinates, where...
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