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The principle of corresponding states (CS principle or CSP) was first formulated by van der Waals, and it says that two fluids (subscript a and z) of a group (e.g. fluids of non-polar molecules) have approximately the same reduced molar volume (or reduced compressibility factor) when compared at the same reduced temperature and reduced pressure ...
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.
For example, air and water; both are fluids and if we consider them together then they can be seen as a stratified fluid system. Density variations in the atmosphere profoundly affect the motion of water and air. Wave phenomena in air flow over the mountains and occurrence of smog are the examples of stratification effect in the atmosphere.
In fluid measurement, the fluid's flow conditions (or flowing conditions) refer to quantities like temperature and static pressure of the metered substance.The flowing conditions are required data in order to calculate the density of the fluid at flowing conditions.
ρ f = Mass density of the fluid; V imm = Immersed volume of body in fluid; ... ρ = fluid mass density; u is the flow velocity vector; E = total volume energy density;
μ is the dynamic viscosity of the fluid (Pa·s = N·s/m 2 = kg/m·s) ρ is the density of the fluid (kg/m 3) Pe is the Peclet Number; Re is the Reynolds Number. The heat transfer analog of the Schmidt number is the Prandtl number (Pr). The ratio of thermal diffusivity to mass diffusivity is the Lewis number (Le).
In many fluid dynamics problems, however, its effect can be neglected. For instance, it is 0 in a monatomic gas at low density (unless the gas is moderately relativistic [3]), whereas in an incompressible flow the volume viscosity is superfluous since it does not appear in the equation of motion. [4]
Mass flow rate is defined by the limit [3] [4] ˙ = =, i.e., the flow of mass m through a surface per unit time t. The overdot on the m 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.