🌈Rainbow Mind Map: Pressure in Fluids & Atmospheric Pressure

Pressure in Fluids and Atmospheric Pressure

Thrust and Pressure

Thrust: Force acting perpendicular to a surface (N)

Pressure: Thrust per unit area (Pascal, Pa)

P = F/A

Where:
P = Pressure (Pa)
F = Force (N)
A = Area (m²)

• Elephant's feet are large to distribute weight (reduce pressure)

• Knife edge has small area to increase pressure

• Snowshoes prevent sinking by increasing contact area

Pressure in Liquid Column

Pressure increases with depth due to weight of fluid above

P = hρg

Where:
P = Pressure (Pa)
h = Height/depth (m)
ρ = Density (kg/m³)
g = Gravity (9.81 m/s²)

• Dams are thicker at the bottom

• Divers experience more pressure at greater depths

• Submarines have strong hulls to withstand pressure

Transmission of Pressure

Pascal's Law: Pressure applied to enclosed fluid is transmitted equally in all directions

Applications:
• Hydraulic lifts
• Hydraulic brakes
• Jacks and presses

Imagine a U-tube with pistons at both ends:

F₁/A₁ = F₂/A₂

Small force on small area can lift large weight on large area!

Atmospheric Pressure

Pressure exerted by Earth's atmosphere (≈101,325 Pa at sea level)

Manifestations:
• Drinking through a straw
• Suction cups
• Barometers

• Ears pop with altitude changes

• Weather systems (high/low pressure)

• Water boils at lower temperature at high altitudes

Variation with Altitude

Atmospheric pressure decreases with increasing altitude

• Altimeters: Measure altitude using pressure

• Weather forecasting: Pressure changes indicate weather patterns

• Aviation: Cabin pressurization needed at high altitudes

Daily Life Examples

Broad dam base: To withstand increasing pressure with depth

Diver's suit: Must withstand high pressure at depth

Syringes: Demonstrate Pascal's principle

• Blood pressure measurement

• Tire pressure

• Scuba diving equipment

• Water towers

Numerical Problems

Problem 1: Calculate pressure at bottom of 10m water tank (ρ=1000kg/m³)

P = hρg = 10 × 1000 × 9.81 = 98,100 Pa

Problem 2: A hydraulic lift has pistons of 0.1m² and 1m². What force on small piston can lift 1000kg on large piston?

F₁/A₁ = F₂/A₂
F₁/0.1 = (1000×9.81)/1
F₁ = 981 N

Problem 3: If pressure at sea level is 1013 hPa and decreases by 12% per km, what's pressure at 3km?

P = 1013 × (0.88)³ ≈ 1013 × 0.68 ≈ 689 hPa

Interactive Rainbow Mind Map on Pressure in Fluids & Atmospheric Pressure

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