Bernoulli's
principle
states that for a fluid with zero viscosity,
an increase in the speed of the fluid occurs simultaneously
with a decrease in pressure
or a decrease in the fluid's potential energy. The principle
is named after Daniel Bernoulli who published it in his book
Hydrodynamica in 1738.
Video
demonstrating Bernoulli's principle using paper  the air
that travels across the top of the paper is moving faster
than the air under the paper. The pressure in the moving stream
is less than the pressure under the paper.
Bernoulli's
principle can be derived from the principle
of conservation of energy.
This states that:
in a steady flow, the sum of all forms of energy in
a fluid along a streamline (family of curves that are
instantaneously tangent to the velocity vector of the
flow) is the same at all points on that streamline.
This requires that the sum of kinetic energy,
potential energy and internal energy remains
constant. This constraint gives rise to a relationship
between the velocity (speed) of the fluid, its pressure,
and its elevation (relative height).
For the mathematical explanation see:
Bernouillis
Equation
Thus an increase in the speed of the
fluid occurs with a simultaneous decrease static
pressure, potential energy and internal energy.
Since there must be conservation
of energy: Increased fluid speed V_{2} with
decrease in internal pressure P_{2} (V_{2}>V_{1}
and P_{2}<P_{1}) 
Bernoulli
and Flight  What contributes to lift in an airplane?
Aircraft wing geometry has a large effect
on the amount of lift The wings of the vehicle have aerofoil*
shaped crosssections and for the given flow conditions the
aerofoil shapes will create a pressure difference between
upper and lower wing surfaces. There will be a high pressure
region underneath and a very low pressure region on top.
*An aerofoil is the term used to describe
the crosssectional shape of an object that, when moved through
a fluid such as air, creates an aerodynamic force
image from NASA.gov
Air flows faster over the top of the wing
decreasing the air pressure. Airflow is slower underneath
the wing so air pressure is greater there contributing to
lift.
The fluid on top of the wing is accelerated
and the fluid on the bottom of the wind is slowed down compared
to velocity of the aircraft itself because the wing geometry
and angle narrows the flow area above the wing and widens
the flow area below the wing from http://physics.stackexchange.com/questions/13030/whydoestheairflowfasteroverthetopofanairfoil.
The concept of lift however is very complicated and cannot
be explained alone using Bernouilli's principle. Newton's
laws are typically preferred over the Bernoulli principle
to explain lift. See References and Readings for further
discussion.
References and Readings
Aviation
Knowledge  Aerofoil
Bernoulli's
Equation  NASA
Lesson:
Bernoulli's Principle K12
Bernoulli
or Newton's Laws for Lift?
