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In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity ¯ (with the usual dimension of length per time), defined as the quotient between the volume flow rate ˙ (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):
where L is the characteristic length, u the local flow velocity, D the mass diffusion coefficient, Re the Reynolds number, Sc the Schmidt number, Pr the Prandtl number, and α the thermal diffusivity, = where k is the thermal conductivity, ρ the density, and c p the specific heat capacity.
M is the local Mach number, u is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and; c is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature.
The Ornstein isomorphism theorem states that, for any given entropy H, there exists a flow φ(x, t), called the Bernoulli flow, such that the flow at time t = 1, i.e. φ(x, 1), is a Bernoulli shift. Furthermore, this flow is unique, up to a constant rescaling of time.
(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 φ V (no standard symbol)
In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol Q (sometimes ˙). It contrasts with mass flow rate, which is the other main type of fluid flow rate.
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Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.