Download Application

Fluids
A fluid is anything that flows (liquid or a gas)
Density
The density ρ of an object is its
mass per unit volume:
The unit for density is kg/m3
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 to a surface
divided by the area A over which the force acts.
Knives, scissors, needles, papercuts…Why are
these items effective in cutting or puncturing?
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.
Derive an expression for the
weight of the water on top of
bottom surface.
h
Fbot
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 / 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?
Explain
Buoyant Force (FB)
The pressure at the top surface
is given by:
The pressure at the bottom
surface is given by:
Archimedes’ Principle
A fluid will apply 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
If ρobject < ρfluid
If ρobject = ρfluid
For a floating object, the fraction that is
submerged is given by the ratio of the object’s
density to that of the fluid.
A plastic cube that measures 2cm on each side has
a density of 706kg/m3. It is connected by a string to
the bottom of the tank filled with water.
a) Find the tension in the string.
b) Determine the acceleration of
the plastic if the string is cut
A geologist finds a rock. He determines the weight
of the rock to be 32.14N while its apparent weight is
25.77N when placed in water. What is the density of
this rock?
A frog in a hemispherical pod finds that he just floats
without sinking in a fluid of density 1.35 g/cm3. If the pod
has a radius of 6.00cm and negligible mass, what is the
mass of the frog?
QUESTIONS: An air-filled balloon is
floating just at the surface of the
water as shown with a solid weight
hanging from it.
a) What is true between the weight of the
system and the buoyant force on the
system?
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.
Brakes,
hydraulics,
syringes, etc
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
air
Where does air pressure come from?
About 99% of atmosphere is below
30km (~20miles)
What is force on piece of paper sitting on table?
Archimedes’ Principle for Gases
This principle also works in the
air; this is why hot-air and helium
balloons rise.
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.
To what length could
water be drawn up a
vertical straw?
Atmospheric Pressure and Gauge Pressure
Most pressure gauges measure the pressure above
the atmospheric pressure – this is called the gauge
pressure.
A car tire is inflated to 35psi. Is
that the gauge pressure?
Example
Each of the four tires of a 1450-kg car have a
gauge pressure of 221 kPa (32.0 lb/in2). How much
area of each tire is in contact with the ground?
Pressure & Boiling
The lower the pressure on a
liquid, the easier it is to make it
boil, i.e., as pressure increases,
so does the boiling pt.
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.
Water circulates throughout a house in a hot-water
heating system. The water is pumped out at a speed
of 0.50m/s through a 4.0cm diameter pipe in the
basement under a pressure of 3.0 atm. It proceeds
5.0m upwards to 2nd floor where it moves through a
2.6cm diameter pipe.
a) Determine the flow speed in smaller pipe.
b) Determine the gauge pressure in smaller pipe
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.