8. Hydrostatics

8.1 Hydrostatics as a part of mechanics

  • Hydrostatics is the study of incompressible fluids that are at rest and in equilibrium.
  • Mechanics also includes the study of fluids in motion, fluid dynamics, but this is one of the most complex branches of mechanics and will not be studied on this course.

8.2 Density

  • Density = mass / volume ρ = m/V
  • In the SI system, density is measured in units of kilograms per cubic meter (kg/m3).
  • The density of water = 1000 kg/m3 and the density of air = 1.2 kg/m3 (atmospheric pressure, 20°C).

8.3 Pressure

  • The application of a force over an area produces pressure.
  • When the force is perpendicular to the surface area, the pressure equals the force divided by the area over which it acts.
  • Pressure = Force / Area P = F/A
  • Pressure is a scalar quantity measured in N/m2 or pascals (Pa) in the SI system
  • A pressure of 1 pascal (Pa) is equivalent to a force of 1 newton acting on each square meter.
  • Pressure can also be measured in atm, bars, millibars, mm Hg, psi ...
  • Atmospheric pressure is surprisingly high: just over 100 kPa

8.4 Archimedes' and Pascal's Principles

  • Archimedes' principle: any completely or partially submerged object experiences an upthrust or buoyant force equal to the weight of the fluid displaced by the object.
  • Pascal's principle: The pressure applied at one point in an enclosed fluid under equilibrium conditions is transmitted equally to all parts of the fluid.