List of equations in fluid mechanics

This article summarizes equations in the theory of fluid mechanics.

Definitions

Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface. Right: The reduction in flux passing through a surface can be visualized by reduction in F or dS equivalently (resolved into components, θ is angle to normal n). F•dS is the component of flux passing though the surface, multiplied by the area of the surface (see dot product). For this reason flux represents physically a flow per unit area.

Here is a unit vector in the direction of the flow/current/flux.

Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension
Flow velocity vector field u m s−1 [L][T]−1
Velocity pseudovector field ω s−1 [T]−1
Volume velocity, volume flux φV (no standard symbol) m3 s−1 [L]3 [T]−1
Mass current per unit volume s (no standard symbol) kg m3 s−1 [M] [L]3 [T]−1
Mass current, mass flow rate Im kg s−1 [M][T]−1
Mass current density jm kg m−2 s−1 [M][L]−2[T]−1
Momentum current Ip kg m s−2 [M][L][T]−2
Momentum current density jp kg m s−2 [M][L][T]−2

Equations

Physical situation Nomenclature Equations
Fluid statics,
pressure gradient
  • r = Position
  • ρ = ρ(r) = Fluid density at gravitational equipotential containing r
  • g = g(r) = Gravitational field strength at point r
  • P = Pressure gradient
Buoyancy equations
  • ρf = Mass density of the fluid
  • Vimm = Immersed volume of body in fluid
  • Fb = Buoyant force
  • Fg = Gravitational force
  • Wapp = Apparent weight of immersed body
  • W = Actual weight of immersed body
Buoyant force

Apparent weight

Bernoulli's equation pconstant is the total pressure at a point on a streamline
Euler equations



Convective acceleration
Navier–Stokes equations

See also

    Sources

    Further reading

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