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Bernoulli Equation: Facts and Misconceptions



In physics we were only taught part of what is necessary to
understand the applications of the Bernoulli equation. This has been the
source of a great many misconceptions which have been propagated. When we
are first introduced to the Bernoulli equation it is always in respect to
a fluid flowing in a pipe with a restriction in it. Since mass must be
conserved the flow through the smaller cross section is faster. Since
energy is conserved the faster flowing fluid has a lower pressure. This is
often all that we were taught. And from this, most of us have come away
with the belief that if air is moving faster it has a lower pressure. On
giving it deeper thought we also might assume that the pressure is lowered
perpendicular to the flow (the static pressure) since we know that if we
put our hand in the path of this faster flowing air we would feel an
increase in pressure.
Because of this point of view some very interesting things have been
taught. First, take the example of a Ping-Pong ball suspended in a
vertical jet of air. The argument is that since the air is moving the
pressure is lower. When the ball moves to the side it comes into contact
with the still air that is of higher pressure. The ball is pushed back
into the flow.
Another example of a common teaching is the "Bernoulli strip" as an
example of lift. The Bernoulli strip is a thin piece of paper that one
blows across the top. It rises into the airstream and is clearly an
example of lift on a wing. The air goes faster over the top, the pressure
is lower and the paper rises.
Before I explain what is missing in our Bernoulli educations, let me
discuss the static port on a small plane. A plane has a small port
somewhere on its side where the static pressure is measured by the
instruments, such as the altimeter. This port provides a fairly accurate
static pressure even though air is passing over it at a high speed. As a
pilot I wondered about this. If one watches the altimeter when the engine
is started up and the propeller blows air across the port, the indicated
altitude does not change. So what is wrong with our understanding of the
Bernoulli effect?
In aeronautics they understand Bernoulli. Ignoring the change in
altitude of any airflow they write the Bernoulli equation:

P(static) + 1/2 roe v^2 = P(total).

The second term is referred to as the "dynamic pressure".
In a confined pipe where energy is constant, total pressure is also
constant so an increase in the dynamic pressure means a decrease in the
static pressure, as we were taught.
In a non-confined space dynamic pressure and static pressure are no
longer linked. So when the propeller gives energy to the air it increases
the dynamic pressure and the total pressure, but not the static pressure.
So at several hundred miles an hour the static port on the airplane still
provides an accurate static pressure measurement.
Let us now look again at the Ping-Pong ball in the jet of air.
First, one might reason that since the jet of air is not confined, and if
it had a lower static pressure, the surrounding air would collapse it
until it had the same static pressure of the surroundings. In fact the
source of the jet of air has only increased the dynamic and total
pressures of the air which is supporting the ball against gravity.
Likewise, ones breath does not have an increased static pressure. Thus
one must look for another explanation for the confined Ping-Pong ball and
the Bernoulli strip.
The answer is in our article on flight
(www.aa.washington.edu/courses/aa101/lift.htm). When the ball is near the
edge of the jet of air, the Coanda causes an asymmetric flow of air around
the ball and momentum transfer causes a force to push the ball back in.
The same is true with the Bernoulli strip. The Coanda effect causes the
air to bend over the hanging paper. Newton's first law says that this
requires a force. His second law says that an equal and opposite force is
exerted on the paper. The paper is lifted.
I hope I have been able to convey the fact that most of the problems
with the Bernoulli effect are caused by our incomplete understanding of
its application. Only in confined fluids are the dynamic and static
pressures coupled.


David Anderson
dfa@fnal.gov