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ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume. For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by
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.
Mass flow rate is defined by the limit [3] [4] ˙ = =, i.e., the flow of mass through a surface per time .. The overdot on ˙ is Newton's notation for a time derivative.Since mass is a scalar quantity, the mass flow rate (the time derivative of mass) is also a scalar quantity.
If mass density is ρ, the mass of the parcel is density multiplied by its volume m = ρA dx. The change in pressure over distance d x is d p and flow velocity v = d x / d t . Apply Newton's second law of motion (force = mass × acceleration) and recognizing that the effective force on the parcel of fluid is − A d p .
The usual normalization of the distribution function is (,) = (,,), = (,), where N is the total number of particles and n is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles.
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.
For a substance X with a specific volume of 0.657 cm 3 /g and a substance Y with a specific volume 0.374 cm 3 /g, the density of each substance can be found by taking the inverse of the specific volume; therefore, substance X has a density of 1.522 g/cm 3 and substance Y has a density of 2.673 g/cm 3. With this information, the specific ...
A general momentum equation is obtained when the conservation relation is applied to momentum. When the intensive property φ is considered as the mass flux (also momentum density), that is, the product of mass density and flow velocity ρu, by substitution into the general continuity equation: