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  2. List of equations in fluid mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_fluid...

    Defining equation SI units Dimension Flow velocity vector field u = (,) ... ρ = fluid mass density; u is the flow velocity vector; E = total volume energy density;

  3. Flow velocity - Wikipedia

    en.wikipedia.org/wiki/Flow_velocity

    In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity [1] [2] in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is scalar, the flow speed.

  4. Stokes' law - Wikipedia

    en.wikipedia.org/wiki/Stokes'_law

    is the flow velocity relative to the object (meters per second). Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' law makes the following assumptions for the behavior of a particle in a fluid: Laminar flow

  5. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Navier–Stokes_equations

    Therefore, the continuity equation for an incompressible fluid reduces further to: = This relationship, =, identifies that the divergence of the flow velocity vector is equal to zero (), which means that for an incompressible fluid the flow velocity field is a solenoidal vector field or a divergence-free vector field.

  6. Hagen–Poiseuille equation - Wikipedia

    en.wikipedia.org/wiki/Hagen–Poiseuille_equation

    where Re is the Reynolds number, ρ is the fluid density, and v is the mean flow velocity, which is half the maximal flow velocity in the case of laminar flow. It proves more useful to define the Reynolds number in terms of the mean flow velocity because this quantity remains well defined even in the case of turbulent flow, whereas the maximal ...

  7. Fluid dynamics - Wikipedia

    en.wikipedia.org/wiki/Fluid_dynamics

    In a compressible fluid, it is convenient to define the total conditions (also called stagnation conditions) for all thermodynamic state properties (such as total temperature, total enthalpy, total speed of sound). These total flow conditions are a function of the fluid velocity and have different values in frames of reference with different ...

  8. Darcy's law - Wikipedia

    en.wikipedia.org/wiki/Darcy's_law

    The flow velocity (u) is related to the flux (q) by the porosity (φ) with the following equation: =. The Darcy's constitutive equation, for single phase (fluid) flow, is the defining equation for absolute permeability (single phase permeability).

  9. Stokes flow - Wikipedia

    en.wikipedia.org/wiki/Stokes_flow

    Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, [1] is a type of fluid flow where advective inertial forces are small compared with viscous forces. [2] The Reynolds number is low, i.e. R e ≪ 1 {\displaystyle \mathrm {Re} \ll 1} .