List of equations in fluid mechanics

This article summarizes equations in the theory of fluid mechanics.


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 through 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 m−3 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


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 alsoEdit


  • P.M. Whelan, M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN 0-7195-3382-1.
  • G. Woan (2010). The Cambridge Handbook of Physics Formulas. Cambridge University Press. ISBN 978-0-521-57507-2.
  • A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 978-0-07-025734-4.
  • R.G. Lerner, G.L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 978-0-07-025734-4.
  • C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN 0-07-051400-3.
  • P.A. Tipler, G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN 978-1-4292-0265-7.
  • L.N. Hand, J.D. Finch (2008). Analytical Mechanics. Cambridge University Press. ISBN 978-0-521-57572-0.
  • T.B. Arkill, C.J. Millar (1974). Mechanics, Vibrations and Waves. John Murray. ISBN 0-7195-2882-8.
  • H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons. ISBN 0-471-90182-2.

Further readingEdit