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.