Bernoulli's Principle

In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy..

V2 > V3 > V1

P1 > P3 > P2

Application of Bernoulli's Principle

• Aerofoil(Racing Car, Aeroplane)

• Bunsen Burner

• Carburetor

An aeroplane , with an aerofoil shape , experoences a lifting force which balance its weight

Explanation of aerofoil

Car Aerodynamic

Archimedes' Principle

Archimedes’ Principle state that “ When an object is immersed in a fluid (a liquid or a gas) ,the buoyant force ( upthrust force) on the object is equal to the weight of fluid displaced by the object.

From Archimedes’ Principle

Buoyant Force, Fb = Weight of fluid displace

= mg (note : F = ma)

= ρVg (note : ρ = m/V )

Thus Fb = ρ V g

Where Fb = Bouyant Force or Upthrust

ρ = Density of fluid

V = Volume of fluid displaced or the volume of the object that immersed in the fluid.

Equation for buoyant force

1. Buoyant force = Weight of fluid displaced
2. Buoyant force = ρVg
3. Buoyant force = Weight object in air – weight in water

Appplication

• Submarine

• Hot Air Ballon

• Hydrometer

• Plimsoll line for ship

Law of Floatation

Pascal's principle

Pascal’s principle states that when pressure is applied to an enclosed fluid, the pressure will be transmitted equally throughout the whole enclosed fluid.

Pascal’s Principle in Mathematical Expression

Input pressure = output pressure
P1 = P2 since, the Pressure , P = Force , F / Area ,A ,therefore

F2 / A1 = F2 / A2

Explaination of hydraulic system

• A small input force, F2 is applied to the small piston resulting in a large output force, F2.
• Based on the Pascal’s Principle, the pressure is transmitted uniformly in all directions,
• When incompressible fluid is moved through a hydraulic system, the volume through which the input system moved must be the same as the volume through which the output system, Hence A1 d1 = A2d2
• Hydraulic systems acts as a force multiplier. They multiply the input force by a certain factor to gain a larger output force.
• The magnitude of the force at the large piston depends on
1. the force, F2, applied to the small piston,

Magnitude of the force = F2 / F1
2. the ratio of the surface area of the piston,

Magnitude of the force = A2 / A1
• A hydraulic system must not contain any air bubbles in any position of its hydraulic fluid system. This will reduce the efficiency of the system as part of the applied force will be used up to compress the air bubbles.

Atmospheric Pressure

Atmospheric pressure is the force per unit area exerted against a surface by the weight of air particles in Earth's atmosphere.

Units of atmospheric pressure:

• 1 atm = 105 Pa
• Barometer mercury gives atmospheric pressure to 76 cm Hg
• Vertical column of water gives atmospheric pressure to 10.3 m.

Effect of height on atmospheric pressure

• Atmospheric pressure depends on the height of a place above sea level and decreases with altitude. At higher altitude, the density and temperature of the air are lower, so the number of collisions between molecules are less and the pressure is lower.

• Atmospheric pressure can be measured by using barometer mercury, barometer Aneroid and barometer Fortin.

Applications

• Rubber sucker

• Drinking straw

• Vacuum cleaner

• Siphon

Measuring Instruments

• Bourdon gauge

• Manometer

• Mercury Barometer

UNDERSTANDING PRESSURE IN LIQUIDS

A liquid in a container exerts pressure because of its weight. For example, if you try to put your finger over the end of a tap when it is turned on, you can feel the pressure of the water in the pipe.

If a fluid (liquid or gas) has a density ρ, its pressure P, at a point due to the fluid of height h, is given by

P = ρgh where g = gravitational acceleration

Therefore, for a given liquid, its pressure:

• increases with depth
• increases with density

For a given point in the fluid, its pressure acts equally in all directions. It does not depend on the shape of containers, only on its depth.

Quiz

Example 1

If the density of sea water is 1150 kgm-3, calculate the pressure below 40m of sea water due to the water alone.

Click for the answer

p=hpg

= 40x1150x10

= 460 000 Pa

= 460 kPa

Introduction of Pressure

Introduction of Pressure

1. Pressure is force per unit area.
2. The SI unit : Nm-2 = Pascal = Pa

take note --> 1 Nm-2 = 1 Pascal

HOW DOES AREA AFFECT PRESSURE?

1. Effect of a force acting over a small area is the production of high pressure over that area.
2. Effect of a force acting over a large area is the production of a lower pressure over that area.

Applications involving High Pressure

1. A sharp knife has a very small surface area on its cutting edge so that high pressure can be exerted to cut the bread.


2. The studs on a football boot have only a small area of contact with the ground. The pressure under the studs is high enough for them to sink into the ground, which gives extra grip.



3. Thumb tack have very sharp ends with very small surface areas. When a force is applied to the head of a thumb tack l, the pressure will drive its sharp end into a piece of paper easily.

Application involving Low Pressure

1. A tractor moving on soft ground has wide tires to reduce the pressure on the ground so that they will not sink into the ground.

2. Skis have a large area to reduce the pressure on the snow so that they do not sink in too far.

3. A wide shoulder pad of a heavy bag will reduce the pressure exerted on the shoulder of the person carrying the bag.