Chapter 9

9.2 - Fluid pressure and temperature

Pressure

What happens to your ears when you ride in an airplane?

What happens if a submarine goes too deep into the ocean?

What happens to your ears when you ride in an airplane?

What happens if a submarine goes too deep into the ocean?

What is Pressure?

Pressure is defined as the measure of how much force is applied over a given area

The SI unit of pressure is the pascal (PA), which is equal to N/m2

105Pa is equal to 1 atm

Pressure is defined as the measure of how much force is applied over a given area

The SI unit of pressure is the pascal (PA), which is equal to N/m2

105Pa is equal to 1 atm

P =FA

Some Pressures

Table 9-2 Some pressures

Location P(Pa)Center of the sun 2 x 1016

Center of Earth 4 x 1011

Bottom of the Pacific Ocean 6 x 107

Atmosphere at sea level 1.01 x 105

Atmosphere at 10 km above sea level 2.8 x 104

Best vacuum in a laboratory 1 x 10-12

Pressure applied to a fluid

When you inflate a balloon/tire etc, pressure increases

Pascal’s Principle Pressure applied to a fluid in a closed

container is transmitted equally to every point of the fluid and to the walls of a container

When you inflate a balloon/tire etc, pressure increases

Pascal’s Principle Pressure applied to a fluid in a closed

container is transmitted equally to every point of the fluid and to the walls of a container

Pinc =F1

A1

=F2

A2

F2 =A2

A1

F1

Lets do a problem

In a hydraulic lift, a 620 N force is exerted on a 0.20 m2 piston in order to support a weight that is placed on a 2.0 m2 piston.

How much pressure is exerted on the narrow piston?

How much weight can the wide piston lift?

In a hydraulic lift, a 620 N force is exerted on a 0.20 m2 piston in order to support a weight that is placed on a 2.0 m2 piston.

How much pressure is exerted on the narrow piston?

How much weight can the wide piston lift?P =

FA

=620N

0.20m2=3.1 ×103Pa

F2 =A2

A1

F1 =2.0m2

0.20m2620N =6.2 ×103N

Pressure varies with depth in a fluid

Water pressure increases with depth. WHY?

At a given depth, the water must support the weight of the water above it

The deeper you are, the more water there is to support

A submarine can only go so deep an withstand the increased pressure

Water pressure increases with depth. WHY?

At a given depth, the water must support the weight of the water above it

The deeper you are, the more water there is to support

A submarine can only go so deep an withstand the increased pressure

The example of a submarine

Lets take a small area on the hull of the submarine

The weight of the entire column of water above that area exerts a force on that area

Lets take a small area on the hull of the submarine

The weight of the entire column of water above that area exerts a force on that areaV =Ah m =ρV

P =FA

=mgA

=ρVgA

=ρAhg

A=ρhg

Fluid Pressure

Gauge Pressure

does not take the pressure of the atmosphere into consideration

Fluid Pressure as a function of depth

Absolute pressure = atmospheric pressure + (density x free-fall acceleration x depth)

Gauge Pressure

does not take the pressure of the atmosphere into consideration

Fluid Pressure as a function of depth

Absolute pressure = atmospheric pressure + (density x free-fall acceleration x depth)

P =FA

=mgA

=ρVgA

=ρAhg

A=ρhg

P =P0 +ρgh

Point to remember

These equations are valid ONLY if the density is the same throughout the

fluid

These equations are valid ONLY if the density is the same throughout the

fluid

The Relationship between Fluid pressure and

buoyant forces

Buoyant forces arise from the differences in fluid pressure between the top and bottom of an immersed object

Buoyant forces arise from the differences in fluid pressure between the top and bottom of an immersed object

Pnet =Pbottom+Ptop =(P0 +ρgh2) −(P0 +ρgh1)

=ρg(h2 −h1) =ρgL

Fnet =PnetA =ρgLA =ρgV =mfg

Atmospheric Pressure

Pressure from the air above The force it exerts on our

body is 200 000N (40 000 lb) Why are we still alive?? Our body cavities are

permeated with fluids and gases that are pushing outward with a pressure equal to that of the atmosphere -> Our bodies are in equilibrium

Pressure from the air above The force it exerts on our

body is 200 000N (40 000 lb) Why are we still alive?? Our body cavities are

permeated with fluids and gases that are pushing outward with a pressure equal to that of the atmosphere -> Our bodies are in equilibrium

Atmospheric

A mercury barometer is commonly used to measure atmospheric pressure

A mercury barometer is commonly used to measure atmospheric pressure

Kinetic Theory of Gases

Gas contains particles that constantly collide with each other and surfaces

When they collide with surfaces, they transfer momentum

The rate of transfer is equal to the force exerted by the gas on the surface

Force per unit time is the gas pressure

Gas contains particles that constantly collide with each other and surfaces

When they collide with surfaces, they transfer momentum

The rate of transfer is equal to the force exerted by the gas on the surface

Force per unit time is the gas pressure

Lets do a Problem

Find the atmospheric pressure at an altitude of 1.0 x 103 m if the air density is constant. Assume that the air density is uniformly 1.29 kg/m3 and P0=1.01 x 105 Pa

Find the atmospheric pressure at an altitude of 1.0 x 103 m if the air density is constant. Assume that the air density is uniformly 1.29 kg/m3 and P0=1.01 x 105 PaP =P0 +ρhg=

1.01 ×105Pa+ 1.29kg/ m3(−1.0 ×103m)(9.81m/ s2)=8.8 ×104Pa

Temperature in a gas

Temperature is the a measure of the average kinetic energy of the particles in a substance

The higher the temperature, the faster the particles move

The faster the particles move, the higher the rate of collisions against a given surface

This results in increased pressure

Temperature is the a measure of the average kinetic energy of the particles in a substance

The higher the temperature, the faster the particles move

The faster the particles move, the higher the rate of collisions against a given surface

This results in increased pressure

HW Assignment

Page 330: Practice 9C, page 331: Section Review

Page 330: Practice 9C, page 331: Section Review

Chapter 9

9.3 - Fluids in Motion

Fluid Flow

Fluid in motion can be characterized in two ways: Laminar: Every particle passes a particular

point along the same smooth path (streamline) traveled by the particles that passed that point earlier

Turbulent: Abrupt changes in velocity Eddy currents: Irregular motion of the fluid

Fluid in motion can be characterized in two ways: Laminar: Every particle passes a particular

point along the same smooth path (streamline) traveled by the particles that passed that point earlier

Turbulent: Abrupt changes in velocity Eddy currents: Irregular motion of the fluid

Ideal Fluid

A fluid that has no internal friction or viscosity and is incompressible Viscosity: The amount of internal friction

within a fluid Viscous fluids loose kinetic energy because

it is transformed into internal energy because of internal friction.

A fluid that has no internal friction or viscosity and is incompressible Viscosity: The amount of internal friction

within a fluid Viscous fluids loose kinetic energy because

it is transformed into internal energy because of internal friction.

Ideal Fluid

Characterized by Steady flow Velocity, density and pressure are constant

at each point in the fluid Nonturbulent

There is no such thing as a perfectly ideal fluid, but the concept does allow us to understand fluid flow better

In this class, we will assume that fluids are ideal fluids unless otherwise stated

Characterized by Steady flow Velocity, density and pressure are constant

at each point in the fluid Nonturbulent

There is no such thing as a perfectly ideal fluid, but the concept does allow us to understand fluid flow better

In this class, we will assume that fluids are ideal fluids unless otherwise stated

Principles of Fluid Flow

If a fluid is flowing through a pipe, the mass flowing into the pipe is equal to the mass flowing out of the pipe

If a fluid is flowing through a pipe, the mass flowing into the pipe is equal to the mass flowing out of the pipe

m1 =m2

ρ1V1 = ρ2V2ρ1A1Δx1 = ρ2A2Δx2ρ1A1v1Δt = ρ2A2v2Δt

A1v1 =A2v2

Pressure and Speed of Flow

In the Pipe shown to the right, water will move faster through the narrow part

There will be an acceleration

This acceleration is due to an unbalanced force

The water pressure will be lower, where the velocity is higher

In the Pipe shown to the right, water will move faster through the narrow part

There will be an acceleration

This acceleration is due to an unbalanced force

The water pressure will be lower, where the velocity is higher

Bernoulli’s Principle

The pressure in a fluid decreases as the fluid’s velocity increases

The pressure in a fluid decreases as the fluid’s velocity increases

Bernoulli’s Equation

Pressure is moving through a pipe with varying cross-section and elevation

Velocity changes, so kinetic energy changes

This can be compensated for by a change in gravitational potential energy or pressure

Pressure is moving through a pipe with varying cross-section and elevation

Velocity changes, so kinetic energy changes

This can be compensated for by a change in gravitational potential energy or pressureP +

12

ρv2 +ρgh=constant

Bernoulli’s Equation

P +12

ρv2 +ρgh=constant

Bernoulli’s Principle: A Special Case

In a horizontal pipe In a horizontal pipe

P1 +12

ρ1v2 =P2 +

12

ρ2v2

The Ideal Gas Law

kB is a constant called the Boltzmann’s constant and has been experimentally determined to be 1.38 x 10-23 J/K

kB is a constant called the Boltzmann’s constant and has been experimentally determined to be 1.38 x 10-23 J/K

PV =NkBT

Ideal Gas Law Cont’d

If the number of particles is constant then:

Alternate Form:

m=mass of each particle, M=N x m Total Mass of the gas

If the number of particles is constant then:

Alternate Form:

m=mass of each particle, M=N x m Total Mass of the gas

P1V1T1

=P2V2

T2

P =MKBT

mV=

MV

Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃

kBT

m=

ρkBT

m

Real Gas

An ideal gas can be described by the ideal gas law

Real gases depart from ideal gas behavior at high pressures and low temperatures.

An ideal gas can be described by the ideal gas law

Real gases depart from ideal gas behavior at high pressures and low temperatures.