Daniel Bernoulli (Groningen, 8 February 1700
- Basel, March 17, 1782) was a Dutch mathematician, member of a family of
talented mathematicians, physicists and philosophers. It is particularly
remembered for his applications of mathematics to mechanics, especially fluid
mechanics, and the first to understand the atmospheric pressure in molecular
terms.
He was a contemporary and close
friend of Leonard Euler. He moved to St. Petersburg in 1724, as professor of
mathematics, but was unhappy there, and an illness in 1733 gave him an excuse
to withdraw. He returned to the University of Basel, where he held the chair of
successive medicine, metaphysics and natural philosophy until his death.
Daniel Bernoulli.
Bernoulli principle
It was exposed by Daniel Bernoulli in
his book Hydrodynamics (1738) and expresses an ideal fluid (no viscosity or
friction) regime in circulation for a closed conduit, the energy that holds the
fluid remains constant along its route. The energy of a fluid at any point
consists of three components:
Kinetics: the energy is due to the
speed that has the fluid.
Gravitational potential: is the
energy due to the altitude that has a fluid.
Energy flow: is the energy that
contains a fluid due to the pressure you have.
The following equation known as
"Bernoulli equation" (trinomial Bernoulli) consists of these same
terms.
Incompressible
flow equation
To apply the equation should make the
following assumptions:
Viscosity (internal friction) = 0
That is, it is considered that the current line on which is applied in a zone
'non-viscous' fluid.
Constant flow
Although the name is due to Bernoulli
equation, the form outlined above was first presented by Leonhard Euler.
Where;
v is the fluid flow speed at a point on a
streamline,
g is the acceleration due to gravity
z is the elevation of the point above a reference
plane, with the positive z-direction pointing upward – so in the direction
opposite to the gravitational acceleration,
P is the pressure at the chosen point, and
p is the density of the fluid at all points in
the fluid.
Lift Equation
The lift equation is L= ½dv²sCL.
Where;
L is stands for lift,
D is stands for density of air,
V is stands for velocity,
S is stands for surface area of the wing,
CL is stands for Coefficient of lift.
How does it applied
to lift?
Density of air
Higher Density means more air
particles in the air and less density means less air particles in the air. If
the air is denser the wing will create more lift because there are more air
particles moving on top of the wing.
Illustration of the Air density in different
altitudes.
Velocity
If the plane is going faster that
means more air particles are moving over the wing in less time generating more
lift. If the plane is going slower that means there are less air particles
moving over the wing in more time, creating less lift. This is why planes run
on the runway to take off.
Area of the wing
If the area of the wing is
larger it can hold more air particles and create more lift. If the area is
smaller it will hold fewer particles on the wing which will result in less
lift. This is why gliders have long wings and they create lots of lift without
any thrust.
Coefficient of lift
It depends on the shape of the
wing. If the wing has deep camber it will create more lift because it forces
the air move faster over the wing. If you have a square shape wing it will
create no lift at all because all air will hit the front and there will be
barely any air flowing on top of the wing. Smooth wing creates more lift
because the air particles will able to move freely and faster.
Importance of
Airflow
The wing should have faster moving
air on the top of wing, so there can be low pressure and high pressure
difference. The wing should be smooth and clean because it is important to have
laminar air flow on the top of the wing; it helps in creating more lift. Things
such as ice and rust on the wing can destroy the lift and increase the stall
speed. If the wing is not smooth it can slow down the air on the top of wing
causing turbulence and it will destroy the lift.
Wind acting on the wing.
Improvement in
Design
By increasing the surface area of the
wing we could of got more lift because there will be more air particles moving
on wing resulting in the lift. We could improve it by increasing the camber and
smoothing the wing more, so there will be less parasite drag.
Characteristics of
the wing
Deep camber.
High Lift.
Low speed.
Thick wing section.
Suitable for
transport and bombers.
How lift is applies to Bernoulli's
principle?
There are stream tubes in the air. The amount air that enters
from the front of tube the same amount wants to leave from back of the tube. If
you place wing in tube there is less room for air to move, so the air start to
move faster on the top of the wing because of the camber and it create low
pressure on the top and because the wing is straight from the bottom and the
air does not speed up a the bottom which create high pressure. The low pressure
on the top of wing want to suck the wing upwards creating lift. Low pressure on
the top of wing also decreases the temperature which can lead up to icing on
the wing. One of main reasons to increase stall speed and lose in lift is
icing. If you fly in clouds, you increase the chances of icing on the wing
because of the moisture in the air. The high speed moving air on top of wing
creates low temperature and it end up freezing all the water vapor in the air
over the wing. Same thing happens in a carburetor, as the mixture in carburetor
speeds up it freezes and can lead up to icing.
Data and
Observation
Straight level = 4.0 to 4.5 g
15° AOA = 5.3 to 6.0 g
We observed that in straight level
flight wing generates around 4g of lift. However, if we increase the angle of
attack about 15° wing starts to generate around 5.3g of lift. Also, as we
increase the angle of attack the wing start to shake and turbulent
air start to form at trailing edge of wing. By using the
thread on the top of wing we were able to see wing tip vortices.
Lift increased as we changed the
angle of attack because as we increase AOA there is less room on top for air to
move, therefore air start to move faster which creates low pressure over the
wing and high pressure under the wing. By having more low pressure on top of
wing and high pressure under the wing it creates more lift. If you increase AOA
too much, your plane can stall because there will be on air moving over the
wing, the air will hit under the wing and it won’t go on top of the wing. By
increasing the angle of attack more turbulent air also start to form. As the
boundary layer reaches the center the wing air start to lose its speed due to
skin friction of the wing. Due to lose in air speed, turbulent air start to
form at trailing edge of the wing, it start to destroy lift, and makes wing
shake. The wing also experienced wing tip vortices. The vortices were created
because the air on the top of the wing wants to move inwards, while the air on
bottom of the wing wants to move outwards. When the air flows unite at trailing
edge they start to flow contra-wise and it end up creating vortices.
What
else is the Bernoulli principle applied?
Cars
Carburetor
For example, inside a
carburetor is a venturi:
Picture of a
carburetor cut in half. Daniel Bernoulli
The venturi apparatus
is created by Giovanni Battista venturi for measuring flow velocity and flow
rate of a liquid through the incompressible pressure variation during passage
of the liquid through a tube of wider section and then the other narrower
section. This effect is explained by Bernoulli's principle and the principle of
continuity of mass. If the flow of a fluid is constant, but its flow area then
decreases necessarily, its velocity increases.
Venturi’s Principle
Airfoil
In
sports cars such as Formula 1, engineers use the very principles of aerodynamics
to make the car can have both stability and good performance on the track, both
on the straights and in the corners. For these cars are very fast, they are
designed to reduce air resistance and increase the downforce generated by the
body and its attachments, causing them to be really "stuck" to the
floor. To this end they use the airfoils, plates external side deflectors and
diffusers as a measure to reduce air resistance.
Formula 1 car’s, the rear wing generates downforce to the
rear of the car
The
aerofoils operate on the same principles of operation of the wings of an
airplane. The only difference is that airplane wings give support while in
cars, more precisely in Formula 1, provide a down force that holds the car on
the ground.
Closer picture of the airfoil. National Museum of the
United Arab Emirates
The
Airfoils does exist in sport cars as well, but can increase the fuel
consumption of the car. Most often only serves to aesthetics, because it has no
significant influence on vehicle performance.
Buildings
The Bernoulli’s
principle can be applied in buildings too, this wing-shaped building is a National
Museum of the United Arab Emirates, and show the history, culture and more
recently the social and economic transformation of the country. The museum
features five towers shaped wings which protrude a lot of landscape (the
landscape was created artificially) where the buildings are. The towers act as
thermal chimneys, creating currents of cooling without electricity. Fresh air
is captured and released into the air of the museum.
But you don’t want your
building has a wing shaped unintentionally, because when the wind blow, would
do a lot of tension on it, and could destroy the building faster and in other
cases like a bridge is the same thing, you don’t want that flowing away, so is
important know about the Bernoulli’s principle even if you don’t want to make a
wing.
References
Conclusion
The Bernoulli’s principle is really
important for an airplane engineer because is necessary to create a good
airplane, to flight better and do not use so much gas, also is used in
different cases like in big buildings because if it is made a building with a
shape of a wing could be a problem because will create a lot tension in this
build because the air flow and will destroy that.
What I learned is
the shape of a wing is the most important part of the airplane, depends how is
it, the airplane can change a lot the flight characteristics, and this determine what kind a airplane,
and what is your propose.
