Pressure

🧠 Topic 1.8: Pressure

🔹 1. Definition of Pressure

Pressure is defined as the force acting per unit area.

Where:

• ( p ) = pressure (in pascals, Pa)
• ( F ) = force (in newtons, N)
• ( A ) = area (in square metres, m²)

🔹 2. How Pressure Varies with Force and Area

From the equation :

• Increasing force (F) → increases pressure
• Increasing area (A) → decreases pressure

✅ Everyday Examples:

1. High heel vs. flat shoe

   • A high heel has a small area → greater pressure on the floor → can make dents on soft floors.
   • A flat shoe has a large area → smaller pressure → less damage.

2. Sharp knife vs. blunt knife

   • A sharp knife has a smaller contact area at the edge → higher pressure → cuts easily.
   • A blunt knife spreads the same force over a larger area → lower pressure → harder to cut.

3. Snowshoes

   • Snowshoes have a large surface area → smaller pressure on snow → prevents sinking.

4. Drawing pins

   • The pointed end has a tiny area → large pressure to penetrate surfaces.
   • The flat end has a large area → smaller pressure on your thumb, so it doesn’t hurt to push.

🔹 3. Pressure in Liquids

Liquids exert pressure in all directions at a given depth.
This pressure increases with:

• Depth (h) – the deeper you go, the greater the pressure.

• Density (ρ) – denser liquids (like mercury) exert more pressure than lighter ones (like water).

• Gravitational field strength (g) – usually constant on Earth (≈ 9.8 N/kg).

🧩 Explanation:

• At greater depths, there is more liquid above, so the weight of the liquid increases → higher pressure.

• This is why deep-sea submarines are built with very strong walls — the pressure is huge at great depths.

✅ Everyday Examples:

1. Bursting of a dam near the bottom

   • Pressure is greatest at the bottom because depth is greatest.
   • Dams are thicker at the base to resist this pressure.

2. Water fountain

   • When you make a hole at the bottom of a water tank, water shoots out faster than from a hole near the top → pressure is higher at greater depth.

🔹 4. Pressure Equation for Liquids

The change in pressure between two points in a liquid is given by:

Δp = ρ g Δh

Where:

• Δp = change in pressure (Pa)
• ρ = density of the liquid (kg/m³)
• g = gravitational field strength (N/kg)
• Δh = change in depth (m)

This formula shows that pressure increases linearly with depth.

🔹 Example Calculation

Example 1:
Find the pressure at a depth of 5 m in water.

So, the pressure 5 m below the water surface is 49 kPa (above atmospheric pressure).

🔹 Important Points about Pressure in Liquids

• Pressure acts in all directions at a point in a liquid.
• Pressure depends only on depth and density, not on the shape or total volume of the container.
• At the same depth in the same liquid, the pressure is the same everywhere.

⚖️ Units of Pressure

Unit	Symbol	Equivalent
Pascal	Pa	1 Pa = 1 N/m²
Kilopascal	kPa	1 kPa = 1000 Pa
Atmosphere	atm	1 atm ≈ 101,000 Pa
Millimetre of mercury	mmHg	760 mmHg = 1 atm

🧪 Applications of Pressure

1. Hydraulic systems

   • Use liquids to transmit force because liquids are incompressible.

   • Pressure applied at one point is transmitted equally throughout the liquid.

     Used in: car brakes, hydraulic lifts, and jacks.

2. Syringes and pumps

   • Applying force on the plunger increases pressure → pushes the liquid out.

3. Atmospheric pressure

   • Caused by the weight of air above the Earth’s surface (≈ 101 kPa at sea level).
   • Decreases with height → why mountain climbers experience thinner air.

💡 Exam Tips

✅ Always write the formula before substituting values.
✅ Check units — especially when converting cm² → m² (1 m² = 10,000 cm²).
✅ When using Δp=ρgΔh, ensure h is in metres and ρ in kg/m³.
✅ Be clear whether a question is about solids (force/area) or liquids (depth/density) — don’t mix the two formulas.
✅ Remember: Pressure increases with depth, not with the shape of the container!
✅ In calculations, final answers should include units (Pa or kPa).