List of equations in fluid mechanics


This article summarizes equations in the theory of fluid mechanics.

Definitions

Here is a unit vector in the direction of the flow/current/flux.
Quantity symbol/sDefining equationSI unitsDimension
Flow velocity vector fieldum s−1−1
Velocity pseudovector fieldωs−1−1
Volume velocity, volume fluxφV m3 s−13 −1
Mass current per unit volumes kg m−3 s−1 −3 −1
Mass current, mass flow rateImkg s−1−1
Mass current densityjmkg m−2 s−1−2−1
Momentum currentIpkg m s−2−2
Momentum current densityjpkg m s−2−2

Equations

Physical situationNomenclatureEquations
Fluid statics,
pressure gradient		r = Positionρ = ρ = Fluid density at gravitational equipotential containing rg = g = Gravitational field strength at point r
Buoyancy equationsρf = Mass density of the fluidVimm = Immersed volume of body in fluidFb = Buoyant forceFg = Gravitational forceWapp = Apparent weight of immersed bodyW = Actual weight of immersed body
Buoyant force

Apparent weight
Bernoulli's equationpconstant is the total pressure at a point on a streamline
Euler equationsρ = fluid mass densityu is the flow velocity vectorE = total volume energy densityU = internal energy per unit mass of fluidp = pressure' denotes the tensor product





Convective acceleration
Navier–Stokes equationsT'''D = Deviatoric stress tensor
  • = volume density of the body forces acting on the fluid
  • here is the del operator.