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 (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]−1Volume velocity, volume flux φV (no standard symbol) m3 s−1 [L]3 [T]−1Mass 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

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 ρ = fluid mass density u is the flow velocity vector E = total volume energy density U = internal energy per unit mass of fluid p = pressure denotes the tensor product <br/ > Convective acceleration Navier–Stokes equations TD = Deviatoric stress tensor = volume density of the body forces acting on the fluid here is the del operator.

List of equations in fluid mechanics

Bron en licentie