Pressure

Summary

Pressure is the ratio of normal force to area.
- Although both force and area are vectors, pressure is a scalar quantity and has no direction.
- Pressure is a way to describe force in a region of a continuous system.
P = F

A
Units
- The SI unit of pressure is the pascal [Pa = N/m² = kg/ms²].
- One hundred thousand pascals are sometimes called a bar [100,000 Pa = 1 bar].
- The unit atmosphere is 101,325 Pa by definition.
Absolute vs. Gauge
- The pressure of a region, as defined above, is its absolute pressure (P).
- The pressure difference between a system and its environment (P₀) is known as gauge pressure (P_g).
P = P₀ + P_g
Pressure in a fluid (P) at rest …
- is equal to the weight of a column of fluid divided by the area on which it rests, so that it …
  - increases uniformly with depth (h)
  - is directly proportional to the density of the fluid (ρ)
  - depends on the surface pressure (P₀)
  P = P₀ + ρgh
- acts equally in all directions and therefore …
  - exerts a net force perpendicular to any surface that it contacts
Pascal's principle: Pressure changes applied to the surface of an enclosed fluid are transmitted evenly throughout the fluid.
- Hydraulics increase force, but
  
  P₁ = F₁ = F₂ = P₂
  
  A₁ A₂
- decrease distance (since energy is conserved)
  
  W₁ = F₁s₁ = F₂s₂ = W₂