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1. Pressure Generally
Pressure = Force / Perpendicular Area
P = F / A
·
P α F: Pressure
is directly proportional to the force (in newtons, N)
·
P α 1/A: Pressure is inversely proportional to the
perpendicular area (in square
metres, m2)
SI unit of pressure is pascal (Pa)
1 Pa = 1 N m-2
(The pressure of 1 Pa is equivalent to the pressure exerted by 1 squashed
apple spread evenly over an area of 1 m2 – it’s a very small
pressure!)
Pressure exerted by solid = Weight of
Solid / Perpendicular Area
P = Weight / Base Area = mg / A
2. Pressure in Fluid
Pressure in fluid (air and liquid) acts in
all direction.
Pressure in fluid, P = ρgh
P = ρgh (= Pressure due to fluid)
Where, ρ = density of the fluid (in kg m-3)
Where, ρ = density of the fluid (in kg m-3)
g = gravitational strength,
g (in N kg-1 or m s-2)
h = height of column of
fluid above the object (in m)
Basis: P = Weight of Liquid /
Area = WL / AL
where,
WL = mL x g (
mL = ρ x VL (= Density of Liquid x Volume of Liquid)
and,
VL = AL x hL (= Cross-sectional Area x Height of LiquidL
Therefore,
P = WL / AL = mL x g / AL = (ρ x VL x g) / AL
= (ρ x AL x hL
x g) / AL
= ρg hL
When an object is submerged into a liquid, it experiences a pressure totalling the pressure exerted by the liquid,
PL (= ρgh) and the pressure
exerted by the air above the liquid PAtm (atmospheric
pressure):
Ptotal = PL + PAtm
3. Gas Pressure and Atmospheric Pressure
In thermal physics, kinetic molecular model
of matter tells us that all gas at temperature above absolute zero exerts
pressure on its container due to the collisions of the gas particles with the
inner surface of the container. The pressure P exerted depends on the rate and
the force of collisions of its particles which in turn depends on two factors, namely:
Density ρ of the gas
P α ρ, (however, ρ = mass/volume i.e. ρ = m/V)
therefore, P
α 1/V (where mass is a constant)
P = k/V
P1V1 = P2V2 =
constant (Boyle’s Law)
Temperature T of the gas
P α T
therefore, P/T = constant
P1/T1 =
P2/T2 =
constant (Pressure Law)
4. Measurement of Pressure
4.1 Measuring
Atmospheric Pressure
4.1.1 Liquid Barometer (e.g. Fortin Barometer with liquid mercury): Just
as in the device called liquid thermometer, we use column of liquid due to
thermal expansion to measure temperature: in the device called liquid barometer, we use column of
liquid supported by air pressure to measure atmospheric pressure.
Fortin Barometer
4.1.2 Aneroid Barometer:
4.1.2.1 to measure atmospheric
pressure by using the contraction or expansion of air in a sealed chamber
to move the pointer along a calibrated scale
4.1.2.2 to foretell weather
– a sudden drop of atmospheric pressure foretells that rain clouds are fast
forming above the barometer
4.1.2.3 to use as altimeter
to measure altitude because at higher altitude, air pressure will be lower and
this can be calibrated to measure altitude
 |
| Aneroid Barometer |
4.2. Measuring
Gas Pressure
4.2.1 Liquid Manometer: This device uses
differential pressure to push liquid (mercury, oil, etc.) of known density up
or down one arm of a U-tube relative to the other arm. If pressure of the arm
connected to the gas is higher than atmospheric pressure, then the liquid in
open arm which is exposed to atmospheric pressure will be pushed upwards.
Then, the pressure of the gas in the
closed arm
=
Atm. Pressure + Pressure Measured by Column of Liquid in the Open Arm.
 |
| Manometer |
4.1.2 Bourdon Gauge: This device uses the gas
pressure to press against a copper coil which will cause the movement of a
calibrated pointer to measure the gas pressure.
5. Pascal’s Principle – Uniform Transmission
of Pressure in Enclosed Liquid
Pascal’s Principle
states that:
“Pressure exerted on an enclosed liquid is transmitted equally
throughout the liquid”
Meaning
of Pascal’s Principle:
§ Energy can
be transferred from one place to another by the use of liquid pressure
§ A large force can be created by a small force
Applications
of Pascal’s Principle in Hydraulic System
§ Hydraulic
Jacks:
§ Hydraulic
Brakes
§ Hydraulic
Pumps
6. Archimedes’
Principle – Buoyant Force Due to Weight of Fluid Displaced
Archimedes’ Principle
states that:
“An object, whether wholly or partially, immersed, in a fluid
is acted on by a buoyant force,
which is equal to the weight of the
fluid displaced”
Meaning
of Archimedes’ Principle:
§
Buoyant Force = Reduction in weight of object
immersed in fluid
=
Weight of fluid displaced
§
Buoyant Force Due to Fluid, Fbuoyant
= ρgV (contrast: Pfluid = ρgh)
Applications
of Archimedes Principle:
Law of Flotation: A floating object displaces its
own weight of fluid in which it floats.
Weight of floating
object = Weight of fluid displaced (Wobject
= Wfluid)
Mass of floating object = Mass of fluid displaced (since, gMobject = gMfluid)
Ship: It floats because the volume of water
displaced has weight equals to the weight of the ship.
Hydrometer: This device floats to different depths in liquids of densities. It is
calibrated to measure relative density of liquids such as milk and
accumulators.
Submarine:
Hot-Air
Balloon
Cartesian Diver
7. Bernoulli’s
Principle – Differential Pressure Due to Differential Flow of Fluid – Fast Flow
Creates Low Pressure
Bernoulli’s Principle
states that:
“In a steady flow of fluid, the pressure of the fluid decreases when the velocity of the fluid increases – and the converse is also true”
Meaning
of Bernoulli’s Principle:
§ Region of
faster fluid flow = Region of lower pressure
§ Region of slower fluid flow = Region of higher pressure which will exert a force on
region of faster fluid flow or low fluid pressure
Natural Phenomena that Demonstrate Bernoulli’s
Principle:
§ Canvas roof of fast-moving vehicle bulges upwards but is flat when vehicle is at rest.
§ Spinning ball curves while non-spinning ball moves straight.
Venturi Tube that Demonstrates Bernoulli’s
Principle:
A venturi tube is a pipe that has a temporary narrowing somewhere in the middle to reduce the pressure and increase the velocity...
§ Upright Venturi Tube with liquid flowing through – liquid flows faster through the narrow
part therefore creating lower pressure which support shorter column of liquid in
the narrow tube above it.
§ Upright Venturi Tube with air flowing through – air flows faster through the narrow part
therefore creating lower pressure which offers lesser support to the ping-pong
ball above the narrow tube.
§ Inverted Venturi Tube with air flowing through – air flows faster through the narrow part
therefore creating lower pressure which allows higher column of liquid to rise
up the tube below it.
Applications
of Bernoulli’s Principle:
§ Aerofoil:
§ Hydrofoil
§ Bunsen Burner
§ Insecticide Sprayer
§ Carburettor
§ Ski Jumper Curving His Body
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