(Note: Boldface words are basic mathematical terms that you will need to know in order to understand this reading. They are explained in the Mathematical Glossary. In introducing this lesson, your teacher will discuss these and other important math terms that are new to members of your class.)
Although flight is a common means of transportation, it remains a mystery to many who use it. While airplanes are a complicated engineering feat, the principles that allow flight are relatively simple.
The first concept to understand is pressure differentials (see the Glossary for Activity 3). An example of this concept is drinking through a straw. Sucking on the straw causes a lower pressure at the top of the straw than the pressure of the atmosphere, which is the pressure pushing on the liquid at the bottom of the straw. This difference in pressures causes the liquid to flow from the higher pressure to the lower pressure and into your mouth.
In the eighteenth century, Daniel Bernoulli, a Swiss scientist, discovered that the velocity of a flow and its pressure were related. This is one of the principles that explains why planes can fly. Just as the higher pressure on the liquid at the bottom of a straw makes the liquid flow into your mouth, a higher pressure on the bottom of an airplane wing, if we can achieve it, will create lift in the wing. Thus, if we can get the right difference in speed of air flow above and below the wing, the wing will have lift and will allow the airplane to fly. As your teacher will demonstrate in class, a properly constructed airfoil will produce the desired difference in speed of air flow.
Bernoulli's equation states:
where
P1 = pressure on top of the wing
P2 = pressure on bottom of the wing
V = air density, a constant
V1 - air velocity on top of the wing
V2 = air velocity on bottom of the wing
gh1 = force of gravity x height at top of wing
gh2 = force of gravity x height at bottom of wing
The symbol for air density is the capital Greek letter upsilon; gh1 and gh2 are essentially the same; and h is the height above the ground. The subscripts indicate values above the wing (subscript 1) and below it (subscript 2).
The correct solution of the equation will show that the faster air flow has a lower pressure.
PROBLEM
A plane is flying at an altitude of 1000 meters (m) above the ground. The density of the air is 1.123 kg/m3, the velocity (speed) of the air on the top of the wing is 60 m/s, the velocity on the bottom of the wing is 30 m/s, and the pressure on top of the wing is 88,6000 pascals.
Let subscript 1 represent the top of the wing and subscript 2 the bottom. Since the plane is flying at 1000 meters (m), the desired height from the ground to the top and bottom of the wing is about the same; therefor h1 = h2.
p1 = 88,600 pascals
Y = 1.12 kg/m3
V1 = 60 meters/second
V2 = 30 meters/second
Find P2. Solution:
1. Use Bernoulli's equation:
This is Bernoulli's equation without the germs gh1 and gh2. Since these quantities are essentially equal, the two sides of the equation are equal without them.
2. Multiply both sides of the quotation by the same quantity, 
Now multiply each term by
Now reduce to lowest terms. We have not gotten ride of some unwanted terms, and we will remove the denominator from the term for P2, the unknown we are solving for:
3. Subtract the same quantity, , from both sides. The term containing P2 will now be the only term on its side of the equation:
4. To get P2 alone on one side of the equation, divide both sides by 2:
5. For ease of computation, factor out : 
SUBSTITUTING:
6. 88,600 + 1.12/2 (602 - 302) = P2
P2 = 90,112 pascals
CONCLUSION:
The pressure below the wing is much greater than the pressure above the wing. Thus, the pressure differential keeps the plane airborne.
Figure 1: Airflow Over and Under an Airfoil
Figure 2: Forces Acting on an Airplane in Flight
1. High Angle of Attack
2. Medium Angle of Attack
3. Low Angle of Attack
Figure 3: Angles of Attack | 
