Fluids

AP/IB Physics

Fluids

• Substances that flow– Liquids– Gases

• Characteristics– Pressure– Viscosity

• Liquid Characteristics– Adhesion & Cohesion– Surface Tension– Capillary Action

• Gas Characteristics– Compressibility

Fluid Statics

• Pressure

• Boyle’s Law

• Pascal’s Principle

• Archimedes’ Principle

Pressure

• Force per unit area– Pascal = N/m2 (english sys: psi)

• Results from the weight of the fluid above

Pressure

• Force per unit area– Pascal = N/m2 (english sys: psi)

• Results from the weight of the fluid above

Pressure

• Force per unit area– Pascal = N/m2 (english sys: psi)

• Results from the weight of the fluid above– pure water

• 1 L = 1 kg = 9.80 N• 1 ft3 = 62.4 lbs

– seawater (average) • 1 L = 1.03 kg = 10.095 N• 1 ft3 = 64 lbs

Pressure

• Air is 0.1% as dense as water

• Atmosphere 52 miles high

• Pressure at sea level– 1 atm = 14.7 psi = 1 kg/cm2 = 1x105 P

• 1 atm = 10 m of seawater

Pascal’s Principle

• Pressure exerted in a fluid is the same in all directions

Pascal’s Principle

• Connect a large & small syringe via a plastic tube.– Depress first one plunger then the other.

• Which one is easier? Why?• Which one moves farther (in relation to the other)?

Why?

– Fill the system with water & repeat the experiment.

• Why is it very bad to have air bubbles in your car’s brake lines?

Pascal’s Principle

• Pressure exerted on a fluid in a closed system is the same throughout the system

Boyle’s Law

• Gases Only– Pressure exerted on the outside of a gas is

inversely proportional to the volume of the gas, if its temperature remains constant.

Pressure = Volume Pressure = Volume

P1 = V2

P2 V1

Archimedes’ Principle

• Weigh a fishing weight using a spring scale.

• Weigh it once again, but immersed in water.– What is the buoyant force on the weight?– How much water is displaced by the weight?– What is the weight of the water displaced?– Compare buoyant force to weight of water

displaced.

Archimedes’ Principle

• Any object that is immersed in a fluid, in whole or in part, will be buoyed up by a force equal to the weight of the fluid displaced.

Archimedes’ Principle

• Buoyant Force– Upward force exerted on an object by a fluid in which

it is immersed

Archimedes’ Principle

• States of Buoyancy– Positive– Neutral– Negative

Archimedes’ Principle

• An object will sink into a fluid until it displaces an amount of the fluid equal to its own weight.

Archimedes’ Principle

• Float– Object weighs less than the fluid it displaces

• Sink– Object weighs more than the fluid it displaces

Fluid Dynamics

• Continuity

• Bernoulli’s Principle

Continuity Equation

• A given system of flowing fluid, not gaining or losing fluid

• Choose two points – same amount of fluid passes each point in a given time

1A1v1 = 2A2v2

Continuity Equation

• Most gases readily compress, most fluids do not• Equation of Continuity for an Incompressible

Fluid

A1v1 = A2v2

Bernoulli’s Principle

• Work-Energy theorem applied to fluids• Relationship between pressure, speed, & height

Bernoulli’s Principle

• Work-Energy theorem applied to fluids

• Relationship between pressure, speed, & height

• General Equation for taking into account changes in height and speed

P1 + ½v12 + gy1 = P2 + ½v2

2 + gy2

Bernoulli’s Principle

• Faster moving air exerts less pressure

Torricelli’s Law

• An application of Bernoulli’s Principle

v2 = 2gh