SPM Physics - Solid and fluid pressure

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