Deriving Bernoulli's Equation and How This Effects the Flight of Airplanes

Flying is one of today's main forms of transportation. People use planes to fly for business, entertainment, and leisure. Air travel is relied on by thousands of people on a daily basis to get from one place to another. Without it, we would be limited to the places we could go, and very few people would ever have the opportunity to go to other countries. So for these reasons and many more, the math behind how these planes fly is very important to all of the world, whether they realize it or not.

Daniel Bernoulli was born into a family of mathematicians, therefore being destined to be one himself. He was born in the Netherlands in the early 1700's. Bernoulli began college at the age of 13 at Basel University and completed his doctorate there in medicine. Upon graduation, he moved to Venice to study mathematics. He went on to publish several mathematical writings, which won him awards such as the Paris Academy Award. Bernoulli became one of the world's most well-known mathematician, infamous for deriving the Bernoulli's Equation.

The Bernoulli's Equation is most known for its application to how airplanes fly. The first Law of Thermodynamics is often expressed as below.
Potential Energy + Kinetic Energy = Constant
PE + ½ mV­² = K

Bernoulli's equation is a case of this equation. In the case of a fluid or gas, static pressure is used to represent potential energy. The kinetic energy is a function of air motion and its density. Bernoulli's equation is usually stated "Static Pressure plus Dynamic Pressure is Constant". Thus one form of the Bernoulli's equation is:
P_s + ½ pV² = K
The equation basically tells us that, as the flow of a fluid moves from one point to another, an increase in speed will be accompanied by a decrease in pressure. There are several forms of this equation.