Fluids Lab 1 – Lecture Notes
1. Bernoulli Equation
2. PitotStatic Tube
3. Airspeed Measurement
4. Pressure Nondimensionalization
Reading: Anderson 3.2, 1.5
Bernoulli Equation
Definition
For
every
point
s
along
a
streamline in constantdensity
frictionless ﬂow, the local speed
V
(
s
) =

�
V

and local pressure
p
(
s
)
are related by
the
Bernoulli Equation
1
p
+
ρ V
2
=
p
o
(1)
2
This
p
o
is a constant
for
all points along
the streamline, even though
p
and
V
may
vary.
This is illustrated in the plot
of
p
(
s
)
and
p
o
(
s
)
along
a
streamline near
a
wing, for
instance.
s
p
p
o
2
V
ρ
1
2
s
Standard terminology is
as
follows.
p
=
static
pressure
1
2
ρV
2
=
dynamic
pressure
p
o
=
stagnation
pressure, or
total pressure
Also,
a commonlyused
shorthand
for
the
dynamic
pressure
is
1
q
≡
ρV
2
2
so we can also
write the Bernoulli
equation
in
the
following
compact
form.
p
+
q
=
p
o
1
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Uniform Upstream Flow Case
V
(
x, y, z
) =
V
∞
Many
practical ﬂow
situations have uniform ﬂow somewhere upstream, with
�
�
and
p
(
x, y, z
) =
p
∞
at
every
upstream point. This uniform ﬂow can be either
at
rest with
�
V
∞
�
V
∞
≃
0 (as
in a
reservoir), or
be moving
with uniform velocity
�
= 0
(as in a
upstream
wind tunnel section), as shown in the figure.
V = 0
Reservoir/Jet
Wind Tunnel
V =
const.
const.
p =
const.
p =
V(x,y,z)
p(x,y,z)
V(x,y,z)
p(x,y,z)
In these
situations,
p
o
is
the
same
for all streamlines,
and can be evaluated using the upstream
conditions
in
equation
(1).
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 Fall '05
 MarkDrela
 Stagnation pressure, Static pressure, Airspeed indicator, Pitot tube, Bernoulli equation, Position error

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