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 A1x1  2 A2x2
1 A1 v1t  2 A2 v2t
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.