1. Introduction to Pressure

Imagine placing a brick on a soft foam. The brick squishes the foam because it pushes on a small area with its whole weight. That push per unit area is called pressure. Everything around you solids, liquids, gases applies pressure.

Definition of Pressure

Pressure is thrust (force acting perpendicular to a surface) per unit area.

Pressure=ForceArea\text{Pressure} = \frac{\text{Force}}{\text{Area}}Pressure=AreaForce

SI unit: Pascal (Pa) or N/m².

Why pressure matters

Solids exert pressure on the surface below them.

Liquids exert pressure on the walls and bottom of their container.

Gases exert pressure on anything they touch (like the air pushing on a postcard).

2. Pressure in Solids, Liquids, and Gases

Pressure by solids

When a brick sits on foam, its weight pushes down, creating pressure. More weight or smaller area = more pressure.

Pressure by liquids

Liquids exert pressure in all directions, not just downward.
Example: A pipe bursts because water pushes outward on its walls.

Pressure by gases

Gases also press on surfaces.
Example: Air pushes a postcard upward when the wind flows under it.

3. Fluids and Their Behavior

Liquids and gases are called fluids because they flow.
Fluids always exert pressure on:

bottom
walls
any object placed inside them

Experiment example: A balloon placed underwater is pushed upward by water pressure.

4. Transmission of Pressure in Fluids

Why solids don’t transmit pressure

In solids, molecules are tightly packed. If you press one side, only that part feels pressure.

Why liquids and gases do

Their molecules can move.
Pressure applied at one point in a closed fluid spreads equally through the entire fluid.

Syringe experiment

Syringe with water: Hard to compress.
Syringe with air: Easy to compress at first because gases have more space between molecules.

Important point

Liquids are nearly incompressible, so they transmit pressure very effectively.
Gases need to be compressed first to transmit pressure similarly.

5. Pascal’s Law

Pascal’s Law Definition

When pressure is applied at one point in an enclosed liquid, it is transmitted equally in all directions.

Verification Diagram Explanation

A vessel has four pistons A, B, C, D of different sizes.
Push piston A → All other pistons move outward.
This proves the same pressure is transmitted everywhere.

Formula

F1/A1=F2/A2

Where:

F1: Force on small piston

A1: Area of small piston

F2: Output force

A2: Area of large piston

Larger the area A2, larger the force F2.

6. Hydraulic Machines

Hydraulic machines work using Pascal’s law.
They magnify a small force into a large force.

Basic Structure

Two pistons connected by a pipe
Filled with a non-compressible fluid (oil/water)
Small piston = input
Big piston = output

Hydraulic Machine Formula

F2=f1*A2/A1

Force multiplies because area of big piston is larger.

Examples of Hydraulic Machines

1. Hydraulic Lift

Used in:

Dentists' chairs
Car repair workshops

A small push on the pedal applies pressure to fluid → Big piston lifts heavy weight.

2. Hydraulic Brake System

Used in cars and bikes.
Pressing the brake pedal applies pressure to brake fluid → Large force presses brake pads → vehicle stops.

3. Hydraulic Jack

Used to lift cars. Pushing the lever repeatedly pumps oil under the lifting piston.

4. Hydraulic Press

Used to:

press metal
compress materials
fit machine parts
punch holes

7. Upthrust (Buoyant Force)

Definition

Upthrust is the upward force a fluid applies on an object immersed in it.

SI unit: Newton (N)

Reason for Upthrust

Pressure increases with depth.
Bottom of object has higher pressure than top → Net upward force.

Examples

Empty bottle floats because upthrust > weight
Bottle filled with water sinks because weight > upthrust
Bucket in well feels lighter inside water because upthrust reduces apparent weight
Airplane experiences upthrust from air

Real Weight & Apparent Weight

Weight in air = real weight

Weight in water = apparent weight

Upthrust = real weight minus apparent weight

Differences

Pressure in Solids vs Liquids vs Gases

PropertySolidsLiquidsGasesMolecule structureVery closeLess closeVery farPressure directionOnly downwardAll directionsAll directionsCompressibleNoAlmost noYesPressure transmissionNoYesYes (after compression)

Hydraulic Machines vs Normal Machines

Hydraulic MachineNormal MachineUses liquidsUses mechanical partsBased on Pascal’s lawBased on mechanical advantageMultiplies force easilyMultiplies force limitedly

Pressure