Lecture 14
Pascal’s Principle
(Chap. 13)
Gases
Atmospheric Pressure
(Chapter 14)
Midterm Exam 1 on Mon. October 4
(Chapters 2-8,10-14; Lectures 1-15)
26-Sep-10
Floating & Liquid Density
The greater the
density of a liquid,
the greater the
buoyant force on
objects floating or
immersed in the
liquid.
26-Sep-10
Floating in Great Salt Lake,
Utah is easy because the
lake water is dense due to
high concentration of salt.
Iceberg: ρ(ice)<ρ(water)
An Iceberg is floating in the ocean. As the iceberg melts, does the
ocean level 1) rise, 2) sink, or 3) stay the same.
As ice, the iceberg displaces a
volume of water equal in mass
to the iceberg’s mass. Once it
is melted, the iceberg still
displaces a volume of water
equal in mass to the original
iceberg (melting doesn’t change
the iceberg mass).
h
Demo: Hydrometer
Hydrometer is a calibrated float; denser the
liquid, the higher the hydrometer floats.
26-Sep-10
Density & Winemaking
Diagram A represents a test jar full of grape
juice before the yeast is pitched. The
hydrometer is floating high because the
liquid is "heavy" with all the sugar... the
hydrometer is pushed up because of the
high fluid density.
A
26-Sep-10
As yeast turns sugar into alcohol and
carbon dioxide, the wine becomes lighter
(alcohol weighs less per unit volume) and
the hydrometer doesn't float as high.
Diagram B represents wine that has
fermented to dryness and is lighter than
water.”
B
www.grapestompers.com
Pascal’s Principle
If an external pressure is applied to a confined
fluid, pressure at every point within the fluid
increases by that amount. This principle is used,
for example, in hydraulic lifts:
Pascal’s Principle:
Work-Energy
Force F1 needed
on piston of area
A1 = 0.04m2 to
lift 5000N car on
piston of area A2
= 4 m2?
Need pressure P2 = 5000N/4m2 = P1 = F1/(0.04m2)
Thus F1 = (0.04m2/4m2)(5000N)=50N
Gases
Gases are the easiest state of matter to
describe, as all ideal gases exhibit similar
behavior.
An ideal gas is one that has low enough
density, and is far enough away from
condensing to liquid, that the interactions
between molecules can be ignored.
Gas atoms or molecules move independently,
with speed that depends on temperature.
Air
Most common example of a gas is air, which
is mixture of nitrogen and oxygen gases
Density of water = 1000 kg/m3
(1 gram per cubic centimeter)
Density of air =
1 kg/m3
(0.001 gram per cubic centimeter)
Water is about 1000 times denser than air
Weight of air is small but not negligible. For example,
weight of air in this room is comparable to your weight
(volume of room about 1000x your volume).
26-Sep-10
Atmosphere
We live at the bottom of an ocean of fluid—the fluid
is air & “ocean” is the atmosphere.
Density of air in the
atmosphere
decreases with
increasing altitude.
Most of atmosphere in
the first 10 km
(about 6 miles) of
altitude.
26-Sep-10
Atmospheric Pressure
Atmospheric column of air
Base: 1 square meter
Height: 10 km (10,000 m)
Volume: 10,000 cubic meters
Mass: 10,000 kilograms
Weight: 100,000 Newtons
(= 22,000 lb = 11 tons)
Pressure: 100,000 Pascals
(= 15 lb per sq. inch)
26-Sep-10
Atmospheric Pressure
Atmospheric pressure is due to the weight of the
atmosphere above us.
Pa = 101 kPa
This is standard atmospheric pressure at sea
level. It declines with altitude above sea level.
Location
San Francisco
Denver, Co
Mt. Whitney
Mt. Everest
Pat (kPa)
101
84
60
35
Atmospheric Pressure
There are a number of different ways to
describe atmospheric pressure.
In pascals:
In pounds per square inch:
In bars:
In inches of mercury: 29.9 in Hg
Weather Report Barometer
•
•
•
•
•
•
Apparent 52°
Dew Point 44°
Humidity 76%
Wind S/5 mph
Visibility 10 mi
Barometer 30.03 in Hg (slightly high)
Sensitivity to Pressure
• Atmospheric pressure does
not crush us, as our cells
maintain an internal pressure
that balances it.
• Since atmospheric pressure
acts uniformly in all directions,
we don’t usually notice it.
• We notice when internal and
external pressures are
different - pressure difference
on ear when descending in
airplane, etc.
Plastic bottle
closed at 2,000 m
altitude & brought
to sea level.
Example - Tire Pressure Gauge
Expert Quality, handy-size
tyre pressure gauge - range
2.0-99.5 PSI (15-700 kPa)
Reads gauge pressure of air in tires. Actual
pressure would be Pg+Patm.
Typical tires: Pg= 30 PSI = 205 kPa
P = 44.7 PSI = 305 kPa
Demo: Magdeburg Hemispheres
Pair of hemispheres
fit together with
air-tight seal
Most of the air is
pumped out from
the interior.
Air pressure holds
the two pieces
tightly together.
26-Sep-10
A
A
L
A
A
A - Atmospheric pressure
L
- Low pressure
Check Yourself
The surface area of a Magdeburg hemisphere is
about 1/100th of a square meter. If we evacuate
the air from inside a pair, how large is the force
holding them together (Atmospheric pressure is
100,000 Newtons per square meter)?
What if only 90% of the air is removed?
26-Sep-10
Crush the Rail Tanker Car
Interior of tank car was
washed out & cleaned
with steam. Then all
outlet valves were shut
and tank car was
sealed.
Workers went home;
when they returned, this
is what they found.
Apparently as tank car
cooled, it collapsed.
The shell on these tank
cars is 7/16th inch thick
steel.
26-Sep-10
Demo: Drinking Straw
With lungs, you reduce
pressure in your mouth and
in the straw.
The higher pressure on the
outside pushes the liquid up
the straw.
Force due to the pressure
difference must match or
exceed the weight.
NO “SUCKING” FORCE
26-Sep-10
L
A
Weight
A
Boyle’s Law
Density of a gas
increases as it is
compressed (volume
decreased)
As the density of a gas
increases, the
pressure in the gas
also increases.
Gauge
Syringe
Tank
Compress the gas by
pushing in the syringe.
Dial gauge shows
increase in pressure.
26-Sep-10
Breathing & Boyle’s Law
A
A
H
L
26-Sep-10
Demo: Stop the Funnel
Water will not enter an air-tight container.
A
A
Weight
Weight
Block exit hole
H
A
A
26-Sep-10
Buoyancy in Air
Objects can float in air, just as they float in
water, if the objects’ average density is
less than the density of air.
Hot Air Balloon
26-Sep-10
Helium-filled Blimp
Fluids in Motion: Flow and Continuity
If the flow of a fluid is smooth, it is called streamline or
laminar flow (a). We will work with laminar flow.
Above a certain speed, the flow becomes turbulent (b).
Turbulent flow has eddies; the viscosity (friction) of the fluid
is much greater when eddies are present.
Flow Rate and the Equation of Continuity
Look at fluid flowing in a tube or pipe.
The mass of fluid that passes any two points in
a pipe or tube must be equal.
“What goes in must come out”
We call this principle “continuity of flow.”
Flow Rate and the Equation of Continuity
If the density doesn’t change – typical for
liquids – continuity requires
where A is area and v is speed. Where the pipe
is wider, the flow is slower.
Equation of Continuity
for Liquids.
Four-lane highway merges to two-lane. Officer in police car
observes 8 cars passing per second, at 30 mph. How many
cars does officer on motorcycle observe passing per second?
A) 4 B) 8 C) 16
How fast must cars in two-lane section be going?
A) 15 mph B) 30 mph C) 60 mph
Water Pipe
Water is flowing continuously in the pipe shown below.
Where is the velocity of the water greatest?
A)
B)
A
C)
B
D) equal everywhere
C
Example
A horizontal pipe contains water at a pressure of
110 kPa flowing with a speed of 1.4 m/s. When
the pipe narrows to one-half its original radius,
what is the speed?
vf Af = vi Ai
vf = vi Ai/Af = vi[πri2]/[π(ri/2)2] = 4vi
vf = 5.6 m/s
Key Points of Lecture 14
• Pascal’s Principle
• Gases
• Atmospheric Pressure and Related Effects
• Buoyancy in Gases
• Fluid in Motion - Continuity
z Before next lecture, read Hewitt Chap. 14, first 2/3.
z Homework Assignment #10 is due before 11:00 PM on
Tuesday, Sept. 26.
z Homework Assignment #11 is due before 11:00 PM on
Friday, Oct. 1.