There are many theories of how lift is generated.
Unfortunately, many of the theories found in encyclopedias, on web
sites, and even in some textbooks are incorrect, causing unnecessary
confusion for students.
The theory described on this slide is often seen on web sites and
in popular literature. The theory is based on the idea that the airfoil
upper surface is shaped to act as a nozzle which accelerates the flow.
Such a nozzle configuration
is called a Venturi nozzle and it can be analyzed
classically. Considering the
conservation of mass,
the mass flowing past any point in the nozzle is a constant;
the mass flow rate
of a Venturi nozzle is a constant.
The mass flow rate m dot is equal to the
densityr times the
velocity V times the flow area A:
m dot = r * V * A = constant
For a constant density, decreasing the area increases the velocity.
Turning to the incorrect airfoil theory,
the top of the airfoil is curved, which constricts the flow.
Since the area is decreased, the velocity over the top of the
foil is increased.
Then from Bernoulli's
equation, higher velocity produces a lower pressure on the
upper surface. The low pressure over the upper surface of
the airfoil produces the lift.
Before considering what is wrong with this theory, let's investigate
the actual flow around an airfoil by doing a couple of experiments
using a Java simulator which is solving the correct
flow equations. Below the simulator
is a text box with instructions. Be sure that the slider on the right
of the text box is pulled to the top to begin the experiments
Let's use the information we've just learned to evaluate the
various parts of the "Venturi" Theory.
The theory is based on an analysis of a Venturi nozzle. But
an airfoil is not a Venturi nozzle. There is no phantom
surface to produce the other half of the nozzle. In our experiments
we've noted that the velocity gradually decreases as you move away
from the airfoil eventually approaching the free stream velocity.
This is not the velocity found along the centerline of a
nozzle which is typically higher than the velocity along the wall.
The Venturi analysis cannot predict the lift generated by a
flat plate. The leading edge of a flat plate presents no constriction
to the flow so there is really no "nozzle" formed. One could
argue that a "nozzle" occurs when the angle of the flat plate is negative.
But as we have seen in Experiment #2, this produces a negative lift.
The velocity actually slows down on the upper surface at a negative
angle of attack; it does not speed up as expected from the
nozzle model.
This theory deals with only the pressure and velocity along
the upper surface of the airfoil. It neglects the shape of the
lower surface. If this theory were correct, we could have any
shape we want for the lower surface, and the lift would be the
same. This obviously is not the way it works - the lower surface
does contribute to the lift generated by an airfoil. (In fact, one
of the other incorrect theories proposed
that only the lower surface produces lift!)
The part of the theory about Bernoulli's equation and a
difference in pressure existing across the airfoil is
correct. In fact, this theory is very appealing because
there are parts of the theory that are correct. In our discussions
on pressure-area integration to
determine the force on a body immersed in a fluid, we mentioned
that if we knew the velocity, we could obtain the pressure and
determine the force. The problem with the "Venturi" theory is that
it attempts to provide us with the velocity based on an incorrect
assumption (the constriction of the flow produces the velocity
field). We can calculate a velocity based on this assumption, and
use Bernoulli's equation to compute the pressure, and perform the
pressure-area calculation and the answer we get does not agree
with the lift that we measure for a given airfoil.
You can download your own copy of the program to run off-line by clicking on this button:
