Solid And Fluid Pressure
Form 4 Physics (SPM) – Chapter 3
Solid Pressure Magnitude of force acting on a given area Pressure, P = Force, F / Area, A unit = Nm-2
or Pascal, Pa Although force is a vector quantity, pressure
is a scalar quantity. This is because experimentally, pressure acts
equally in all directions, producing no net direction
Fluid Pressure Pressure that results from the collision of
particles in fluid Particle collision are mostly elastic, thus
conserving kinetic energy and momentum (mv) The change in direction after collision results in
a rate of change in momentum, producing impulsive force.
This force acts on a given area, produces pressure
Increasing depth of fluid (amount of fluid) and its density increases particle collision, resulting in increasing pressure
Pressure, P = h ρ g where depth of fluid = h, density of fluid = ρ, acceleration due to gravity = g
Unit = kgm-1s-2 or Pascal (Pa) Other units commonly used:
PSI (pounds per square inch) – Imperial system Bar atm (where 1 atm = 105 Pa = 76cmHg) mmHg/cmHg/mmH2O/cmH2O
Atmospheric Pressure (Patm) Pressure exerted by the particles in the
atmosphere on every surface on Earth Changes with altitude because the density of
the atmosphere changes with altitude. (Density and therefore pressure decreases as altitude increases)
Patm at sea level (average height of ocean) ≈1 X 105 Pa
Patm at peak of Mt. Everest ≈3.33 X 104 Pa
In tubes A, B, C, D and E, the height of level of water is identical because pressure is equal in all tubes (Patm)
This shows that pressure is not influenced by the shape or orientation of the tube
The instrument used to measure atmospheric pressure is known as a barometer. (Baro = pressure)
Types of barometers: Mercury barometer Aneroid barometer
Simple liquid barometer
Fluid used in barometer has to have the following properties: Incompressible Does not evaporate easily Does not stick to the wall of the barometer
Ideal fluid to be used is mercury (Hg)
Atmospheric pressure is measured byPatm = <Height of column><Name of fluid>
Patm = 76cmHg
To convert cmHg to the S.I. unit, Pa:Patm = hρg
Patm = (76/100) X 1.36x103(density of Hg) X 10
Patm = 1x105 Pa
If water is used in substitute for mercury, the column height can be calculated:
Patm = hρg
1x105 = h X 1x103 X 10105 = h X 104
h = 10m Having a column height of 10m makes the
water barometer unfitting and immobile.
Aneroid barometer
Atmospheric pressure is applied in: Sucker hooks Drinking straws Evaluating altitude (altimeter) Baking with yeast Breathing Heimlich maneuver
Gas pressure (Pgas) Pressure exerted by gas particles on
surrounding surfaces Measured by an instrument known as a
manometer (U-tube) In a manometer, the fluid pressure at one
point in one arm is equal to the pressure at another point in the opposite arm at the same level, where the type of fluid is the same
Manometer
Level of fluid on both sides is the same as both ends are exerted by the same pressure, Patm
When Pgas > Patm
Gas
h
Pgas = Patm + hρg
When Pgas < Patm
Gas
h
Pgas = Patm - hρg
Bourdon gauge
Transfer of pressure within static fluid When an object is submerged in a fluid, it experiences
equal pressure from all directions. The pressure is transferred equally in the fluid in all directions.
Hence, neglecting pressure changes due to depth, the pressure at any given point within the fluid is constant.
Pascal’s Principle In a closed system of fluids, any pressure exerted is equally
distributed throughout the fluid and remains constant Characteristics of the hydraulic fluid:
Incompressible Does not adhere to the surface of the system Is not volatile
Simple Hydraulic Lift
Since pressure is evenly distributed,P1 = P2
Thus, F1/A1 = F2/A2
When one piston is depressed, the other piston rises. This occurs as the volume displaced by the fluid from the first piston occupies the space at the second piston
V1 = V2
Thus, d1A1 = d2A2
where A = surface area of piston, d = distance moved by piston
Applications of Pascal’s Principle: Hydraulic jacks Hydraulic robots and machinery Vehicle brakes and steering
Support due to pressure in fluids With reference to Newton’s Law of Motion, every
action of force has a normal that acts in the opposing direction.
Weight is a force and has a normal support on solid ground. When an object is immersed in fluid, the normal support is produced from the pressure differential at the upper and lower surface of the object.
This supportive force provides floatation and is known as buoyancy.
Archimedes’ Principle When an object is partially or completely immersed in a
fluid, the weight of the fluid displaced is equivalent to the buoyant force that supports the object
Buoyant force, B = V ρ g, where V volume of immersed part of the object, ρ = density of fluid, g = acceleration due to gravity
Buoyant force is also equivalent to weight of object when not immersed (true weight) – weight of object when immersed (apparent weight)
B = Wt - Wa
An object sinks when Wt > B
An object floats when Wt = B
In a uniformly distributed fluid, buoyant force remains constant regardless of depth of fluid.
Buoyant force changes in direct proportion to fluid density.
Fluid density increases when Temperature decreases Concentration increases Pressure increases Mass increases
Applications on Archimedes’ Principle Submarine Plimsoll Scale on the hull ships Hot air balloon Hydrometer Cartesian diver Measuring volume of kings’ crowns using a bath
tub and an old genius
Differential pressure in fluid flow
High fluid pressure Low fluid pressure
Direction of motion
Fp vt vf
Imagine a particle moving uniformly in a fluid of gradually decreasing pressure. The pressure behind the particle is greater than the pressure in front.
A force (Fp)will be produced in the direction of motion resulting in acceleration of the particle, thus the velocity of the accelerating particle at the back (vt) is greater than at the front (vf).
This shows that pressure and velocity are inversely related
Bernoulli’s Principle Pressure and velocity of a fluid are inversely
proportional as a result of the fluid flowing in a curved streamline.
Aerofoil
In fluid mechanics, it is generally accepted that liquids and gases flow in arranged packets known as streamlines.
An aerofoil has an aerodynamic shape which is meant to redirect air streamlines in order to minimise resistance and produce lift
Curvature of the streamline occurs when the air is passed above the aerofoil due to the shape of the aerofoil.
The curvature decreases the air velocity of the streamline above the aerofoil resulting in the pressure below the aerofoil to be greater than above.
The differential pressure produces the aerodynamic lift.
The greater the curvature of the streamline, the greater the decrease in velocity.
The streamline curvature above the aerofoil can be increased by increasing the angle of attack (the angle at which the aerofoil meets the streamline)
However, if the angle of attack is too large, the streamlines about the aerofoil could converge and dissipate. This diminishes the lift, an event known as stall.
Aircraft wings can deploy slats and flaps to increase surface area to give extra lift for take off or to increase air resistance to provide additional drag for landing and decelerating.
Slats
Flaps
Bernoulli’s water tower
Flow direction
As flow velocity increases, pressure at base of tube decreases from left to right
Venturi nozzle
Venturi nozzle
Venturi nozzle causes great increase in flow velocity, hence great decrease in pressure
Observations of Bernoulli’s Principle Wings of airplane Sail of a boat Hydrofoils of boat Insecticide dispenser Mesocyclone Whirlpools