Download Archimedes` Principle & Density

Fluids
A fluid is anything that flows (liquid or a gas)
Density
Material
Aluminium
Gold
Ice
Water
Oil
Air
Helium
Density (kg /m3)
2700
19300
917
1000
800
1.29
0.179
Pressure
Pressure is force acting perpendicular
Pressure in Fluids
Pressure is the same in every
direction in a fluid at a given
depth; if it were not, the fluid
would flow….static
equilibrium.
How is pressure
defined within a fluid?
Consider a beaker of water of
area A and height, h.
The force exerted on top of
water surface will be smaller
than the force at bottom…why?
h
Determine the weight of the
water on top of bottom surface.
In which container would a fish experience more
pressure from the liquid if the fish was at the
bottom of each container?
A
B
C
D
Why doesn’t a giraffe’s brain explode when it drinks
from a puddle or faint when it raises its head to such
a large height above the heart? Pressure is height
dependent above or below the heart.
Pressure / Density Questions
1. Why do swimmers float better in the ocean
than in a lake?
2. Why don’t they make longer snorkels so that
people could dive deeper without scuba gear?
3. How do submarines change depth?
4. When ice cubes melt when
floating in water, does the water
level rise, fall, or remain the same?
Atmospheric Pressure
At sea level the atmospheric
pressure is about 101.3kPa. This is
called one atmosphere (1 atm). We
also know this as 14.7 lb/in2.
30km
Where does air pressure come from?
What is force on piece of paper sitting on table?
Atmospheric Pressure and Gauge Pressure
Most pressure gauges measure the pressure
above the atmospheric pressure –
The absolute pressure is
Barometer
A mercury barometer is used to
measure atmospheric pressure. The
height of the column of mercury is
such that the pressure in the tube at
the surface level is 1 atm.
Example
A very long tube with a radius of 0.300cm is placed in
a tightly fitting hole in the top of wine barrel with a
radius of 20.0cm and filled to the lid with water. If
water is filled in the tube to a height of 12.0m the
barrel bursts.
a) What is the mass of the water column in the tube?
b) What is the net force on the lid of the barrel?
To what length could
water be drawn up a
vertical straw?
Pressure & Boiling
Buoyant Force (FB)
The pressure at the top surface
is given by:
The pressure at the bottom
surface is given by:
Archimedes’ Principle
Any fluid applies a buoyant force to an object that is
partially or completely immersed in it; the magnitude
of the
If the FB > mobjectg
If the mobjectg > FB (max),
Archimedes’ Principle & Density
If ρobject > ρfluid then object will sink.
If ρobject < ρfluid then object will float.
If ρobject = ρfluid then object can be anywhere
in fluid (fish).
For a floating object, the fraction that is
submerged is given by the ratio of the object’s
density to that of the fluid.
Archimedes’ Principle for Gases
This principle also works in
the air; this is why hot-air and
helium balloons rise.
We have a buoyant force on
us from the atmosphere.
A geologist finds a rock. He determines the
mass of the rock to be 3.28kg while its apparent
mass is 2.63kg when placed in water. What is
the density of this rock?
QUESTIONS: An air-filled balloon is
floating near the surface of the water
with a solid weight hanging from it.
a) What is true between
the hanging weight and
buoyant force on balloon?
b) What if balloon is given
a large shove downward
and then let go. Describe
the subsequent motion of
balloon.
Consider a boat loaded with scrap iron in a
swimming pool. If the iron is thrown overboard
into the pool, will the water level at the edge of the
pool rise, fall, or remain unchanged?
Pascal’s Principle
Any change in pressure
applied to a completely
enclosed fluid is transmitted
undiminished to all parts of
the fluid and the closed walls.
Fluids in Motion
Equation of continuity
The volume flow rate
(Av) has the same value
at every point along a
tube that has a single
entry and exit point for
the fluid flow. For two
positions…
Example
Calculate the mass flow rate of blood (1.0g/cm3) in an
aorta with cross sectional area 2.0cm2 if the flow
speed is 0.40m/s.
Bernoulli’s Principle
• In steady flow for an incompressible fluid, the
density ρ, the pressure P, the fluid velocity v and
elevation y are related through
Note on Bernoulli equation
When a problem asks for gauge pressure,
it wants the Patm subtracted out.
When calculating P1 or P2 this is the
ABSOLUTE pressure. To find GAUGE
pressure, you need to subtract away Patm.
Pabs = Patm + Pgauge
Example
If wind blows at 24.5m/s over the
roof of a house, what is the NET
force on the roof if it has an area
of 335m2?
As wind blows over top, what
happens to pressure on
outside? Inside?
Application: Air moves faster over top of wing, slower
beneath. This leads to lower pressure over wing and
is one of factors that contributes to uplift of plane.
Application: Curve ball, air on one side of spinning
ball faster than the other (leads to pressure
difference)
Application: Atomizers, spray bottles, lawn sprayers
Determine an expression for the speed at which water leaves
the tank which is a height h below the surface.