Transcript PhysCh9.79
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 is Pressure?
Pressure is defined as the measure of how
much force is applied over a given area
F
P
A
The SI unit of pressure is the pascal (PA),
which is equal to N/m2
105Pa is equal to 1 atm
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
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?
P
F2
F
620N
3
3.1
10
Pa
2
A 0.20m
A2
A1
F1
2.0m
2
0.20m
2
3
620N 6.2 10 N
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
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
V Ah
P
m V
F mg Vg Ahg
hg
A
A
A
A
Fluid Pressure
Gauge Pressure
P
F mg Vg Ahg
hg
A
A
A
A
does not take the pressure of the atmosphere into
consideration
Fluid Pressure as a function of depth
P P0 gh
Absolute pressure = atmospheric pressure +
(density x free-fall acceleration x depth)
Point to remember
These equations are valid ONLY if the
density is the same throughout the fluid
The Relationship between Fluid
pressure and buoyant forces
Pnet Pbottom Ptop (P0 gh2) (P0 gh1)
g(h2 h1) gL
Fnet Pnet A gLA gV m f g
Buoyant forces arise from the differences in
fluid pressure between the top and bottom of
an immersed object
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
Atmospheric
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
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
P P0 hg
5
3
3
2
1.01 10 Pa 1.29kg / m (1.0 10 m)(9.81m / s )
8.8 104 Pa
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
HW Assignment
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
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.
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
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
m1 m2
1 V1 2 V2
1 A1x1 2 A2x2
1 A1 v1t 2 A2 v2t
A1 v1 A2 v2
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
Bernoulli’s Principle
The pressure in a fluid decreases as the
fluid’s velocity increases
Bernoulli’s Equation
Pressure is moving through
a pipe with varying crosssection and elevation
Velocity changes, so kinetic
energy changes
This can be compensated
for by a change in
gravitational potential
energy or pressure
1 2
P v gh cons tan t
2
Bernoulli’s Equation
1 2
P v gh cons tan t
2
Bernoulli’s Principle: A Special Case
In a horizontal pipe
1
1
2
2
P1 1 v P2 2 v
2
2
The Ideal Gas Law
PV NkB T
kB is a constant called the Boltzmann’s
constant and has been experimentally
determined to be 1.38 x 10-23 J/K
Ideal Gas Law Cont’d
If the number of particles is constant then:
P1 V1
T1
P2 V2
T2
Alternate Form:
P
MK BT
mV
Ê
ÁM
Á
Á
Á
ÁV
Ë
ˆ˜ kB T kB T
˜˜
˜˜
m
¯ m
m=mass of each particle, M=N x m Total Mass of the gas
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.