AA311 Homework 3. Due October 17, 2011
Give all your answers in SI units.
Problem 1.
Recall that, when developing the equations for the ISA and the notion of “geopotential
height,” we assumed that
g
(
h
G
)
≈
g
0
. The geopotential height
h
was then deﬁned such that
ΔPE(
h
) = ΔPE(
h
G
)
⇒
h
=
±
r
earth
r
earth
+
h
G
²
h
G
This is a “zeroth order” approximation of the
true
acceleration due to gravity
g
(
h
G
) =
g
0
±
1
1 + (
h
G
/r
earth
)
²
2
A “ﬁrst order” approximation is
g
(
h
G
)
≈
g
0
±
1

2
h
G
r
earth
²
1. Verify the correctness of this ﬁrst order approximation by expanding
f
(
±
) =
±
1
1 +
±
²
2
in a Taylor series about
±
= 0. Show the ﬁrst three terms (i.e., to quadratic order in
±
).
2. Develop an expression for a new altitude
˜
h
(
h
G
) deﬁned such that ΔPE(
˜
h
) = ΔPE(
h
G
) where
ΔPE(
˜
h
) =
Z
˜
h
0
m g
0
1

2
˜
h
r
earth
!
d
˜
h
Problem 2.
In a certain wind tunnel, the speed in the circular test section with radius 25 centimeters is
100 m/s. What is the speed upstream of the test section where the radius is 1 meter?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Aerodynamics, hG hG

Click to edit the document details