CHAPTER: PRESSURE AND HYDRAULICS

1. Introduction to Pressure

Concept

When a force acts on a surface, its effect depends not only on the force but also on the area over which it acts.

Example:
If you place a brick on soft foam, it sinks because its weight acts on a small area.
If you place the brick flat, it sinks less because the same force acts on a larger area.

This effect is called pressure.

Definition

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

Pressure= Force/Area

SI Unit

Pascal (Pa)

1 pa = 1N/m2

Importance of Pressure

• Solids exert pressure on the surface below them.
• Liquids exert pressure on the walls and bottom of containers.
• Gases exert pressure on everything they touch (example: air pressure).

2. Pressure in Solids, Liquids and Gases

(A) Pressure in Solids

• Solids exert pressure only in the downward direction.
• More force → more pressure.
• Smaller area → more pressure.

Examples:

• Sharp knife cuts easily.
• High heel sinks in soil.
• Camel has broad feet to reduce pressure.

(B) Pressure in Liquids

• Liquids exert pressure in all directions.
• Liquid pressure increases with depth.
• Depends on:

1. Density of liquid
2. Depth
3. Acceleration due to gravity

Example:

• Dam walls are thicker at the bottom.
• Water pipe bursts outward.

(C) Pressure in Gases

• Gases exert pressure in all directions.
• Gases are compressible.
• Air pressure surrounds us.

Example:

• Balloon expands when filled with air.
• Wind pushes objects.

3. Fluids and Their Behavior

Liquids and gases are called fluids because they can flow.

Fluids exert pressure on:

• Bottom
• Walls
• Any object immersed in them

Example:
A balloon under water experiences upward push due to water pressure.

4. Transmission of Pressure in Fluids

In Solids

• Molecules are tightly packed.
• Pressure does not spread uniformly.

In Liquids and Gases

• Molecules can move.
• Pressure applied at one point spreads equally in all directions.

Important Point

• Liquids are nearly incompressible → transmit pressure effectively.
• Gases are compressible → need compression before effective transmission.

5. Pascal’s Law

Definition

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

Formula

F1/A1 = F2/A2

Where:

• (F1) = Force applied on small piston
• (A1) = Area of small piston
• (F2) = Force on large piston
• (A2) = Area of large piston

If (A2) is larger, then (F2) becomes larger.

6. Hydraulic Machines

Hydraulic machines work on Pascal’s law.

They use:

• Two pistons
• A connecting pipe
• Non-compressible liquid (oil)

Small force → Large force output

Hydraulic Machine Formula

F2​=F1​×A1​A2​​

Force multiplication occurs because the area of the output piston is larger.

Types of Hydraulic Machines

1. Hydraulic Lift

Used in:

• Car workshops
• Dentists’ chairs

Small force lifts heavy loads.

2. Hydraulic Brake

Used in vehicles.

Brake pedal → pressure in brake fluid → large force at brake pads → vehicle stops.

3. Hydraulic Jack

Used to lift cars by pumping oil.

4. Hydraulic Press

Used to:

1. Compress materials
2. Shape metals
3. Punch holes

7. Upthrust (Buoyant Force)

Definition

Upthrust is the upward force exerted by a fluid on an immersed object.

SI Unit

Newton (N)

Cause of Upthrust

• Pressure increases with depth.
  Bottom of object experiences more pressure than top.
  This creates a net upward force.

Examples

• Empty bottle floats → Upthrust > weight
• Filled bottle sinks → Weight > upthrust
• Bucket feels lighter in water
• Airplane gets lift from air (fluid)

Real Weight and Apparent Weight

• Real weight = Weight in air
• Apparent weight = Weight in water

Upthrust=Real weight−Apparent weight

8. Differences

Pressure in Solids, Liquids and Gases

Hydraulic Machines vs Normal Machines

Important Exam Points

• Pressure = Force / Area
• Liquid pressure increases with depth
• Pascal’s law is the principle behind hydraulic machines
• Liquids are incompressible
• Upthrust occurs due to difference in pressure
• Objects float when upthrust ≥ weight