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Chapter 13 : Fluids - LCHS Physical
Science |
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Objectives: The learner will...
...solve fluid problems concerning
pressure, hydraulics and buoyancy
...explain the Bernoulli effect |
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Vocabulary:
fluid : liquid or a gas that
flows
pressure : force of atomic impact across a surface
pascal : unit of pressure equal to a Newton per square meter
buoyant force : a force opposite to the weight of a displaced
volume of fluid
Bernoulli effect : in a moving fluid the greater the velocity
the lower the pressure |
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FLUID & PRESSURE
A fluid is a substance that flows and can be either a liquid or
gas.
Even though air is a gas that weighs very little, the cumulative
effect of the entire earth's atmosphere can add up. If you
could weigh a box of air that was one inch square and as tall
as the top of the atmosphere, it would weigh approximately
14.7 pounds! Pressure is defined as weight per area
( P = F / A ). So, the air pressure on the surface
of the earth (at sea level) is 14.7 pounds per square inch
or 14.7 psi. Other units of pressure measure is Newtons/m²,
Pascal, atmospheres, and mmHg. Here is a conversion table:
| 1 atm |
101325 N/m² or Pascals |
14.7 psi |
760 mmHg |
The unit mmHg relates to the mercury (Hg) barometer. This
device is an evacuated tube filled with mercury that is inverted
into a pan of mercury. The weight of the air at sea level
raises the mercury level in the tube to 760 millimeters. If
this mercury column had a base area of exactly one square
inch it would weigh 14.7 pounds! To convert from psi to
mmHg you would multiply by the conversion factor 760mmHg/14.7psi.
To convert from Pa to psi the factor would be 14.7psi/101325Pa.
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| Water is a fluid that is about 1000 times denser than air
so the effects of pressure are more noticeable at a smaller
change in depth. A box filled with water that is 1 square
inch at the base and 1 foot tall weighs about .4306 pounds.
So for every foot in depth you decend into water the water
pressure increases by .4306 psi. You must also
remember to add the air pressure on top of the water to be
completely correct. The pressure at a 30 foot depth
would then be (30 x .4306) + 14.7 or 27.6 psi. Water
pressure in Pascals is 9800 Pa for each meter
of depth, (adding 101325 Pa for air pressure). |
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HYDRAULICS
| A hydraulic device consists of an incompressible liquid
in 2 connected cylinders. One cylinder has a smaller input
piston and the other cylinder has a much larger output piston.
The pressure is the same throughout the system. A smaller
effort force is exerted on the smaller piston. This smaller
piston also has to move a greater distance. This same pressure
is exerted on the larger piston which can move a much greater
force but only a fraction of the distance. The ratio of the
sizes of the 2 pistons is roughly the factor by which you
can multiply your input effort force! |
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BUOYANCY
| Fluids (both gas and liquid) can exert a buoyant
force on objects immersed in them. When you pull a toy
boat out of a tub you don't expect the impression of the boat
to stay, rather the surrounding water rushes in to fill the
void. If you could freeze the water and then pull out the
boat the impression would stay. It turns out that this impression
would hold a weight of water equal to the boat itself! Another
way to see this is illustrated at the far left. A full beaker
of water overflows into a bucket as a boat is placed within.
The weight of the displaced water equals the weight of the
boat! For objects that sink we must consider the relative
densities and the volume of displaced fluid (immediate left).
A 2 x 2 x 2 cm cube with a density of 3g/cc has a mass
of 24g and a volume of 8cc. As it is submerged it displaces
8cc of water or 8 grams of water. This buoyant force opposes
and reduces the mass scale reading to 16 g! (24 - 8) This
is why it is easier to lift heavy objects under water. |
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Click here
for a BUOYANCY DEMO!
Click here
for a Log float demo!
The Bernoulli Effect
When a fluid flows with increasing velocity the pressure within
the fluid decreases. This doesn't sound very logical at first but
if we realize that when a fluid is pushed to increase it's speed
the atoms of the fluid bump against each other their distance apart
increases. Pressure has to do with the number of atoms colliding
with a unit surface area and if the atoms are farther apart then
fewer atoms collide with the same surface area, decreasing the pressure.
You can demonstrate this effect by blowing across a straw in a liquid
and watch the liquid level within the straw rise. The increased
velocity above the straw lowers the pressure so that the pressure
on the stagnant air above the liquid is relatively greater, thus
pushing the liquid up the straw. You can also blow a stream of air
between 2 suspended sheets of paper. You would expect the sheets
to be blown apart but instead they come together!
Click here for a Bernoulli wing DEMO!
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| Practice: |
Help: |
PB1
What is the pressure (Pa) if 56 Newtons of force is applied to .54
square meters (m^2)?
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P=F/A |
PB2
If a pressure of 64 psi is applied to 49 square inches, what is
the total force (lbs)?
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P=F/A
64=F/49 |
PB3
Convert 63 psi to mmHg.
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x760/14.7
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PB4
Convert 37000 Pascals to psi.
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x14.7/101325 |
PB5
84 lbs. are applied to a 14 square inch piston, if the lift piston
is 42 square inches,
how many pounds can this hydraulic device lift?
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f/a=F/A
84/14=F/42 |
PB6
13 lbs. are applied to a 2.142857 square inch piston, if the weight
to be lifted is 5 pounds,
how square inches is the lift piston on this hydraulic device?
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f/a=F/A
5/A=13/2.142857 |
PB7
Including air pressure, what is the pressure (psi) at a water depth
of 65 feet?
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(65x.4306)+14.7
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PB8
Including air pressure, what is the pressure (Pa) at a water depth
of 22 meters?
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(22x9800)+101325 |
PB9
How many mL of water will overflow a full tub after a 500 cc boat
is 19 % submerged
and then a 46 gram mass is added to the boat?
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(500x.19)+46 |
PB10
What does a mass scale read for a suspended ball with a volume of
64 mL
and a density of 14 g/mL submerged in a liquid of density 2.6 g/mL?
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m=dxV
(14x64)-(2.6x64) |
answer bank:
252
.8241758
3257.143
5.367876
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316925
141
729.6 |
103.7037
3136
42.68607 |
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Scientist Spotlight:
Archimedes
287-212 BC Legend has it that Archimedes discovered his principle
of buoyancy, which states that the buoyancy force is equal to the
weight of the liquid displaced, while taking a bath, upon which he
is supposed to have run naked through the streets of Syracuse shouting
"Eureka!" (I have found it).
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Resources (Study Links/Study Tips/Reading Lists)
Click here for
a BUOYANCY DEMO!
Click here
for a Log float demo!
Click here for
a Bernoulli wing DEMO!
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Chapter 13 : Fluids - LCHS Physical
Science |
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