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Fluid Mechanics in Physics

A fluid pushes in every direction at once, which is why pressure and not force is the natural quantity to work with. It rises steadily with depth, and it rises for a reason that is easy to miss. A deeper parcel of water must carry the weight of everything above it, so the pressure at the bottom of a tank is the same whatever shape the tank is, and only the depth matters. The same idea gives the buoyant force and the reason a steel ship floats. Once the fluid moves, speed and pressure start trading places, and the blocks end with the relation that governs that exchange and the two classic results that come out of it.

Pressure exerted on a surface

Given

  • (N)
  • (m²)
Density of a substance

Given

  • (kg)
  • (m³)
Absolute pressure at a depth in a fluid

Given

  • (Pa)
  • (kg/m³)
  • (m)

Constant used

Gauge pressure at a depth in a fluid

Given

  • (kg/m³)
  • (m)

Constant used

Absolute pressure from a gauge reading

Given

  • (Pa)
  • (Pa)
Specific gravity of a substance

Given

  • (kg/m³)
  • (kg/m³)
Buoyant force on a submerged body

Given

  • (kg/m³)
  • (m³)

Constant used

Apparent weight of a body immersed in a fluid

Given

  • (N)
  • (N)
Fraction of a floating body below the surface

Given

  • (kg/m³)
  • (kg/m³)
Volume flow rate through a pipe

Given

  • (m²)
  • (m/s)
Equation of continuity for an incompressible fluid

Given

  • (m² and m/s)
  • (m² and m/s)
Speed change through a pipe of changing width

Given

  • (m²)
  • (m/s)
Bernoulli's equation along a streamline

Given

  • (Pa)
  • (kg/m³)
  • (m/s)
  • (m)

Constant used

Bernoulli's equation for a horizontal pipe

Given

  • (Pa)
  • (m/s)
  • (kg/m³)
Speed of fluid leaving a hole in a tank

Given

  • (m)

Constant used

Lift from the pressure difference across a wing

Given

  • (Pa)
  • (m²)