# INTRODUCTION

Bernoulli’s principle and equation were first introduced in 1738. Even so, they were only applied to flight in December of 1903, when the Wright brothers invented and flew the first airplane successfully. As of today, this principle is used as much as projectile motion is used in flight, pipes, racing car’s front and rear wings, even in a rocket’s exhaust system. With all this being said, it must be acknowledged that this is a highly skillful tool for engineers.

# BERNOULLI’S EQUATIONS

As you can see it’s an equation rather than a formula or function, which gives it the flexibility in finding certain properties, either by solving algebraically or by deriving and integrating. However, in a higher level of physics, you would use lagrangian mechanics (a more complex mathematical approach to mechanics)

● P1 stands for the pressure

● Then the next summation is half the initial pressure times the initial velocity squared

● The next addition is the potential energy formula

Workflow is a stream of molecules going in the horizontal direction, either in curvature or straight line. Bernoulli’s equation starts by adding the flow work to the amount of kinetic energy and the potential energy, which results in a constant. In other words, it is the adding of the mechanical energy of a stream and its flow work that gives you your constant. The first formula given above is more of an equation than it is integrated, therefore you can find the velocity and pressure just by solving algebraically. You can cancel P1 when it isn’t given, and when there isn’t any initial velocity it becomes zero (V1 = 0) canceling the entire kinetic energy expression.

# PRINCIPLE

So the first principle is simply the more pressure there is the less the velocity it has, and the smaller the pressure is the greater the velocity should be added. In fact, that is the same reason why airplanes don’t need to go at maximum speed at takeoff since there is enough atmospheric pressure in the troposphere to take off. The second principle is in the terms of conservation of energy in fluids, potential energy, or fundamentally height; Gravity also plays a role in the pressure and speed of an object in a period of time. In addition to this PE also makes you able to solve algebraically for mass.

# GRAPHICAL INFO

Used for pressurized tubes containing liquids or gases.

This displays a function of a wing under pressure from the lower surface area in turn generating lift.

The angle of attack generates enough drag and lift to equal the net force and can even equate to the weight of the machine for specific engineering purposes.

# CONCLUSION

Bernoulli’s principle is key to understanding drag, aerodynamics, and even thrust since rocket engines generate it from the fuel of certain gases and liquids. Following this, the next step in understanding streams or flow of air is the Navier stokes equation. The Navier stokes equation will be featured in the next article, it explains how cold and hot air take the lagrangian path or the path of least resistance. Understanding it is crucial in aerodynamics.

Sources:

1- “Bernoulli’s Equation Example Problems, Fluid Mechanics – Physics.” *YouTube*, YouTube, 15 Nov. 2017, http://www.youtube.com/watch?v=xTAfyc06ZxQ.

2- “Bernoulli Equation.” *Pressure*, hyperphysics.phy-astr.gsu.edu/hbase/pber.html.

3- Admin. “Bernoulli’s Principle & Equation – Definition, Derivation, Applications, Examples.” *BYJUS*, BYJU’S, 7 Jan. 2021, byjus.com/physics/bernoullis-principle/#:~:text=The%20Bernoulli%20equation%20is%20considered,termed%20as%20the%20Bernoulli%20effect.

Writer: Ali Fathi Al-Bati

Editors: Omar Alturki/Yara Bawazir