Pressure applied to a confined fluid is transmitted equally in all directions
P₁ = P₂ (pressure at any point in a static fluid)
F₁/A₁ = F₂/A₂ (force ratio equals area ratio)
Pascal's Law Applications:
• Hydraulic jacks
• Car brakes
• Hydraulic presses
• Aircraft controls
• Heavy machinery
Key Insight:
Small force over small area creates large force over large area
Hydraulic Press Calculator
Hydraulic Press Formulas:
Mechanical Advantage = F₂/F₁ = A₂/A₁
Work = F₁ × d₁ = F₂ × d₂ (conservation of energy)
d₁/d₂ = A₂/A₁ (displacement ratio is inverse of area ratio)
Hydraulic Press Advantages:
• High mechanical advantage
• Smooth, controlled operation
• Can exert tremendous force
• Self-lubricating system
Common Uses:
• Car lifts in garages
• Industrial forming
• Trash compactors
Fluid Pressure & Hydrostatic Pressure
Hydrostatic Pressure Formula:
P = P₀ + ρgh
Where: P = total pressure, P₀ = surface pressure, ρ = fluid density, g = gravity, h = depth
Pascal's Law: Pressure change at surface transmits throughout fluid
Standard Conditions:
Atmospheric pressure: 101,325 Pa
Gravity: 9.81 m/s²
Pressure Units:
1 atm = 101,325 Pa
1 bar = 100,000 Pa
1 psi = 6,895 Pa
Hydraulic System Design
System Design Considerations:
Required Pressure = Load Force / Piston Area
Pump Power = Pressure × Flow Rate / Efficiency
Cylinder Volume = Area × Stroke Length
Cycle Time = Volume / Flow Rate
Design Guidelines:
• Safety factor: 1.5-3.0
• System efficiency: 80-90%
• Working pressure: <350 bar
• Operating temperature: <80°C
Applications:
• Construction equipment
• Manufacturing presses
• Aircraft controls