Air Speed Theory
Eugene M. Cliff
January 22, 2001
1
Introduction
The primary purpose of these notes is to develop the necessary mathematical
machinery to understand pitot-static 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 devel-
opment for a compressible-flow 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 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,
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.
1
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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 where the velocity is zero and at such a point (
p
)
P
(
p
) =
C
. This means
that the constant of integration
C

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- Fluid Dynamics, Airspeed
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