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Monday, 24 December 2012

Forces and Pressure


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)
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 (= Mass of Liquid x g) 
mL = ρ x VL (= Density of Liquid x Volume of Liquid) 
and,           VL = AL x hL (= Cross-sectional Area x Height of Liquid

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.


Barometer_mercury_column_hg.jpg (1704×2415)
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:

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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