Transcript Fluids ppt - My Teacher Pages

Fluids
Honors Physics
Liquids
In a liquid, molecules flow freely from
position to position by sliding over each
other

Have definite volume
Do not have definite shape – conform to
their container
Density
Mass Density
ρ = m/V
 Units – kg/m3

Common densities
Air – 1.29 kg/m3
 Fresh water – 1.00 x 103 kg/m3
 Ice - 0.917 x103 kg/m3

Densities of Common
Substances
Buoyancy
The apparent loss of
weight of an object
that is submerged
The water exerts an
upward force that is
opposite the
direction of gravity
called the buoyant
force.
Submerged
An object placed in water will displace,
or push aside, some of the water
The volume of water displaced, is equal
to the volume of the object
This method can be used to easily
determine the volume of irregularly
shaped objects
Archimedes’ Principle
An immersed object
is buoyed up by a
force equal to the
weight of the fluid it
displaces.
This principle is true
for all fluids.
This means that the
apparent weight of
an immersed object
is its weight in air
minus the weight of
the water it
displaces
For floating objects

FB = Fg (object)
Examples
A brick with a mass
of 2kg weighs 19.6N
If it displaces 1L of
water, what is the
buoyant force
exerted on the
brick?
Buoyant force =
weight of water
displaced
1L displaced = 9.8N
Buoyant force =
9.8N
Sink or Float?
If the buoyant force
acting on an object
is greater than its
weight force, the
object will float
A submerged
objects’ volume, not
mass determines
buoyant force
3 Rules



An object more
dense than the fluid
it is immersed in will
sink
An object less dense
than the fluid it is
immersed in will float
An object with equal
density to the fluid
will neither sink nor
float.
Density & Buoyant
Force
The buoyant force
and apparent weight
of an object
depends on density
Fg (obj ) 

FB
f
Sample Problem 9A
A bargain hunter purchases a “gold”
crown at a flea market. After she gets
home, she hangs the crown from a
scale and finds its weight to be 7.84 N.
She then weighs the crown while it is
immersed in water, and the scale reads
6.86 N. Is the crown make of pure gold?
Explain.
Floatation
Why is it possible for a brick of iron to
sink, but an equal mass of iron shaped
into a hull will float?
When the iron is shaped, it takes up
more space (volume)
Principle of Flotation – A floating object
displaces a weight of fluid equal to its
own weight
Liquid Pressure
Pressure for solids is determined by the
equation P=F/A
In this equation, the force is simply the
weight of the object.
The same principle can be used for
liquids
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 the
container.
F2 = A2 F1
A1
Sample Problem 9B
The small piston of a hydraulic life has
an area of 0.20 m2. A car weighing 1.20
x 104 N sits on a rack mounted on the
large piston. The large piston has an
area of 0.90 m2. How large a force must
be applied to the small piston to support
the car?
Pressure
More dense liquids will produce more
force and, therefore, more pressure.
The higher the column of liquid the
more pressure also.
For liquids,

Pressure = density x g x depth


AKA Gauge Pressure = ρgh
Total pressure = density x g x depth +
atmospheric pressure

P = PO + ρgh
Examples
Is there more water
9m
pressure at 3m or at
9m of depth?
Calculate the
P  (1000kg / m3 )(9.8m / s 2 )(10m)
pressure exerted by
a column of water
=98000 Pa
10m deep.
Sample Problem 9C
Calculate the absolute pressure at an
ocean depth of 1.00 x 103 m. Assume
that the density of the water is 1.025 x
103 kg/m3 and that PO=1.01 x 105 Pa.
Pascal’s Principle
Changes in
pressure at any
point in an enclosed
fluid at rest are
transmitted
undiminished to all
points in the fluid
and act in all
directions.
Hydraulic systems
operate using this
principle.
Gasses
Have neither definite volume nor shape
The atmosphere is a good example of a
gas.
In the atmosphere, the molecules are
energized by sunlight and kept in
continual motion
Atmosphere
The density of the
atmosphere
decreases with
altitude
Most of the Earth’s
atmosphere is
located close to the
planets surface.
Atmospheric Pressure
The atmosphere all
around us exerts
pressure just as if
we were submersed
in a liquid
At sea level, air has
a density of about
1.2 kg per cubic
meter
A column of air, of
1 sq. meter that
extends up through
the atmosphere
weighs about
100,000 N
The avg
atmospheric
pressure a sea
level is 101.3 kPa
Measuring Pressure
A barometer is used to measure
atmospheric pressure
Air pressure forces mercury up the
glass tube, to display the pressure
This process is similar to that of drinking
out of a straw
Boyle’s Law
For a gas, the
product of the
pressure and the
volume remain
constant as long as
the temperature
does not change.
P1V1 = P2V2
Examples
If you squeeze a
balloon to 1/3 its
original volume,
what happens to the
pressure inside?
3x
A swimmer dives
down, until the
pressure is twice the
pressure at the
waters surface. By
how much does the
air in the divers
lungs contract?
2x
Charles’ Law
The volume of a definite quantity of a
gas varies directly with the temperature,
provided the pressure remains constant.
V1T2 = V2T1
Combined Gas Law
When Boyle’s and Charles’ laws are
combined the equation looks like this.
P1V1T2 = P2V2T1
Sample Problem 9E
Pure helium gas is contained in a
leakproof cylinder containing a movable
piston. The initial volume pressure and
temperature of the gas are 15 L, 2.0
atm and 310 K, respectively. If the gas
is rapidly compressed to 12 L and the
pressure increased to 3.5 atm, find the
final temperature of the gas.
Ideal Gas Law
Compares volume, pressure, and
temperature of a gas
PV = NkBT
 P = pressure, V = volume, N = # of mols of
gas particles, kB = Boltzman’s Constant
(1.38x10-23 J/K), T = temperature

Fluid Flow
Smooth flow is said
to be laminar flow
Particles all follow
along a smooth path

Streamline path
Streamlines never
cross
Irregular flow is said
to be turbulent
Irregular motion
produced are called
eddies
Continuity
Continuity says that
the mass of and
ideal fluid flowing
into a pipe must
equal to mass
flowing out of the
pipe.
Or m1 = m2
Because the mass
flowing is
determined by the
cross-sectional area
of the pipe and how
fast it flows, we can
also say
A1v1 = A2v2
Bernoulli’s Principle
Pressure in a fluid decreases as the
fluid’s velocity increases.
Bernoulli’s Principle can be seen in
birds in flight and airplanes
Pressure above the wing is less than
pressure below the wing, creating lift
Bernoulli’s Equation
This is an expression of conservation of
energy in a fluid.
P + ½ρv2 + ρgh = constant
Pressure + kinetic energy per unit
volume + gravitational potential energy
per unit volume = constant along a
given streamline
Sample Problem 9D
A water tank has a spigot near its
bottom. If the top is open to the
atmosphere, determine the speed at
which the water leaves the spigot when
the water level is 0.500m above the
spigot.
We’ll use
 (P + ½ρv2 + ρgh)1 = (P + ½ρv2 + ρgh)2

we assume the water level is dropping slowly, so v2, at
the top, = 0
Also, since both ends are open to the atmosphere P1 =
P2
That simplifies the equation to
P + ½ρv12 + ρgh1 = P + ρgh2 and subtract P
½ρv12 + ρgh1 = ρgh2
ρ is the same throughout, so
½v12 + gh1 = gh2
solve for v
v = √(2g(h2-h1))
plug & chug
v = √(2(9.8 m/s2)(.5m))
v = 3.13 m/s
Pg. 344: 17, 18, 23, 25,
29, 36, 39, 44, 47, 48
Test on Fluids:
Thursday