Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 1, Problem 1.11P
A U-tube mercury manometer is used to measure the pressure at a point on the wing of a wind-tunnel model. One side of the manometer is connected to the model, and the other side is open to the atmosphere. Atmospheric pressure and the density of liquid mercury are
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Consider a column of a planet's atmosphere. The planet's atmosphere is a
compressible ideal gas at rest that obeys the polytropic relation
Po
%3D
3/2
Po
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where pis pressure and pis density. Here, p, and P, are the values of pressure and density,
respectively, at the planet's surface. Take z (altitude) to be positive upward with z=0 at the
surface, take R to be the gas constant for the planet's atmosphere, and take g to be the
downward acceleration due to gravity.
a)
Starting from hydrostatic balance and the polytropic relation above, derive an
expression for the pressure field, p(z), in terms of the given parameters. Leave all
parameters except the polytropic index as algebraic.
b)
Derive an expression for the density field, p(z), in terms of the given parameters.
Leave all parameters except the polytropic index as algebraic.
c)
Derive an expression for the temperature field, T(z), in terms of the given
parameters. Leave all parameters except the polytropic index as algebraic.
The sketch shows an oil manometer that is connected between two pipes which transport water. The density of water can be taken as 998kg/m3, the specific gravity of glycerol is 0.76 and atmospheric pressure is 100 kPa. The respective dimensions (as shown on the sketch) are given below:
h1 = 0.17 m h2 = 350 mm h3 =15cm.
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A balloon filled with helium (of density PHe = 0.164 kg/m³) has a cube shape and rises through the strato-
sphere. Air density is given by p(z) = Pa exp(-9), where pa = 1.225 kg/m³ is the density of air at the
sea level, g = 9.81 m/s² is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant of
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expression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere.
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h = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derive
an expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloon
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I
h
He
9
Chapter 1 Solutions
Fundamentals of Aerodynamics
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