Superficial velocity (or superficial flow velocity), in engineering of

multiphase flow In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve so ...

s and flows in

porous media A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usu ...

, is a hypothetical (artificial)

flow velocity In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity 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 f ...

calculated as if the given phase or fluid were the only one flowing or present in a given cross sectional area. Other phases, particles, the skeleton of the porous medium, etc. present in the channel are disregarded. Superficial velocity is used in many engineering equations because it is the value which is usually readily known and unambiguous, whereas real velocity is often variable from place to place. Superficial velocity can be expressed as: :

u_s = \frac  {A}

where: * u_s - superficial velocity of a given phase, m/s * Q - volume flow rate of the phase, m³/s * A - cross sectional area, m² Using the concept of

porosity Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measur ...

, the dependence between the

advection In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is al ...

velocity and the superficial velocity can be expressed as (for one-dimensional flow): :

u_s = \phi u

where: *

\phi

is porosity, dimensionless *u is the average fluid velocity (excluding the other phase, solids, etc.), m/s. The local physical velocity can still be different than the average fluid velocity because the vector of the local fluid flow does not have to be parallel to that of average flow. Also, there may be local constriction in the flow channel.

See also