Bernoulli’s, Pascal’s, & Archimedes’ Principles Principles of Fluids

Bernoulli’s Principle Chapter 1 Bernoulli’s Principle

Bernoulli’s Principle As the Velocity (speed) of a fluid increases, the Pressure exerted by the fluid decreases Why?

This explains one of the forces that make an Airplane Fly Airplanes have FOUR basic forces acting on them: LIFT can be explained using Bernoulli’s Principle. LIFT THRUST GRAVITY DRAG LIFT THRUST DRAG GRAVITY

Cross section of an Airplane Wing Lower Pressure Higher Pressure

Higher Pressure Lower Pressure

How does Bernoulli’s Principle Explain…. how a vacuum cleaner works, AND how drinking through a straw works?

Venturi Effect As the size of a fluid’s pathway decreases, the velocity of the fluid increases.

Chapter 2 Archimedes' Principle

Buoyant Force The upward force of a Fluid exerted on an object. What is the downward Force exerted on an object? Gravity

Archimedes’ Principle The buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object.

27.0 g Of Object Mass Of Object = 73.0 g L = 3.00 cm W = 3.00 cm Al Volume = 27.00 cm3 Of Object H = 3.00 cm Volume of H2O Displaced = 27.0 ml Mass of H2O Displaced Full beaker = 127.0 g Empty = 100.0 g 27.0 g 100.0g 127.0g

Archimedes (Example #1) Gravity = 73.0 g Negative Buoyancy Buoyant Force = 27.0 g

135.0 g Of Object Mass Of Object = 6.0 g Balloon filled with AIR Volume = 135.0 cm3 Of Object Volume of H2O Displaced = 135.0 ml Mass of H2O Displaced Full beaker = 235.0 g Empty = 100.0 g 135.0 g 100.0g 235.0g

Archimedes (Example #2) Gravity = 6.0 g Positive Buoyancy Buoyant Force = 135.0 g

The Boat begins to enter the water. Mass Of Object = 20,000,000 g Volume Of Object = 40,000,000 cm3 Because the amount of water displaced is still less than the boat’s mass, it continues to sink. The Boat begins to enter the water. Volume of H2O Displaced (so far) = 10,000,000 ml NEW Volume of H2O Displaced = 20,000,000 ml Mass of H2O Displaced Full = 20,000,100.0 g Empty = 100.0 g 20,000,000 g Mass of H2O Displaced Full = 10,000,100.0 g Empty = 100.0 g 10,000,000 g Now that they are equal, it stops sinking. 100.0g 10,000,100g 20,000,100g

Archimedes (Example #3) Gravity = 20,000,000 g Neutral Buoyancy Buoyant Force = 20,000,000g

Chapter 3 Pascal’s Principle

Force P = Area PRESSURE What is pressure? It is a measurement of the force applied over an area. Force P = Area

Pascal’s Principle Pressure applied to one place of a fluid is transmitted unchanged throughout the fluid.

Which side of the problem do we have more information? P = Force Area Area x P = Force x Area Area Force = Pressure x Area Force = 10,000 N Force? Force = 10,000 N Area = 15 cm2 Area = 500 cm2 A B Force = 20 N x 15 cm2 cm2 P = Force Area Force = 300 N P = 10,000 N 500 cm2 Which side of the problem do we have more information? P = 20 N cm2 P = 20 N cm2