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 a model that the airfoil
upper surface is shaped to act as a nozzle which accelerates the flow.
This nozzle configuration
is known as a Venturi nozzle and it can be analyzed
classically. By considering the conservation of
the mass flowing past any point on the airfoil (nozzle) is a constant.
This leads to the relation that the
mass flow rate
(the density times the velocity times the area) of the Venturi is a
constant. For a constant density, at any point where the area is decreased,
the velocity will be increased.
Therefore, over the top of the airfoil the velocity will be increased
due to the flow constriction.
Now, coupling this with Bernoulli's
equation, at any point where the area is decreased the pressure
will be decreased. The low pressure over the upper surface of
the airfoil then 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.
Let's use the information we've just learned to evaluate the
various parts of the "Venturi" Theory.
This 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