Air Speed Theory
Eugene M. Cliff
February 15, 1998
1
Introduction
The primary purpose of these notes is to develop the necessary mathematical
machinery to understand pitotstatic airspeed indicators and several related
notions of airspeed. In the next section we will begin with a model of one
dimensional flow (along a streamline) and carry out the required development
for a compressibleflow form of the Bernoulli equation. From there we will
define a few notions of airspeed and discuss the relations among them.
2
One Dimensional Flow
We consider steady (
no change with time
), frictionless (
no viscous forces
)
flow along a streamline and so we have
d P
ρ
+
d
[
V
2
/
2] +
g dz
= 0
.
(1)
Our goal is to ‘integrate’ this expression.
Note that the real work is the
integration of the first term; this generally requires that we introduce a
P

ρ
relation.
2.1
Case 1: Fluid at Rest
In this case we have
V
≡
0 so that (1) takes the form
d P
=

ρ g dz,
1
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which we recognize as the hydrostatic equilibrium equation used in the inves
tigation of the model atmosphere and altimeter theory. The required
P

ρ
relation came from the perfect gas law and the assumption of a temperature
profile.
2.2
Case 2: Constant Density
In this case we have
ρ
≡
˜
ρ
(
i.e.
a constant) and equ’n (1) can be simply
integrated to yield
P
+ ˜
ρV
2
/
2 + ˜
ρgz
=
C
,
where
C
is a constant along the given streamline. For most aircraft applica
tions we neglect the last term (˜
ρgz
) and write
P
+ ˜
ρV
2
/
2 =
C
.
The constant (
C
) has a fixed value along the streamline; along the line
P
(the static pressure) and
V
(the airspeed) change, but in such a way that the
combined term is constant. We can imagine a place along the (extended) line
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 Fall '09
 Fluid Dynamics, Pressure difference, Airspeed, incompressible flow approximation

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