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In the homogeneous model of two-phase flow, the slip ratio is by definition assumed to be unity (no slip). It is however experimentally observed that the velocity of the gas and liquid phases can be significantly different, depending on the flow pattern (e.g. plug flow, annular flow, bubble flow, stratified flow, slug flow, churn flow). The ...
We notice that the volumetric flow rate is a scalar quantity and that the direction is taken care of by the normal vector of the surface (area) and the volumetric flux (Darcy velocity). In a reservoir model the geometric volume is divided into grid cells, and the area of interest now is the intersectional area between two adjoining cells.
Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity 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 ...
For Reynolds number greater than 4000, the flow is turbulent; the resistance to flow follows the Darcy–Weisbach equation: it is proportional to the square of the mean flow velocity. Over a domain of many orders of magnitude of Re ( 4000 < Re < 10 8 ), the friction factor varies less than one order of magnitude ( 0.006 < f D < 0.06 ).
While a vertical velocity term is not present in the shallow-water equations, note that this velocity is not necessarily zero. This is an important distinction because, for example, the vertical velocity cannot be zero when the floor changes depth, and thus if it were zero only flat floors would be usable with the shallow-water equations.
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.
Then for an ideal gas the compressible Euler equations can be simply expressed in the mechanical or primitive variables specific volume, flow velocity and pressure, by taking the set of the equations for a thermodynamic system and modifying the energy equation into a pressure equation through this mechanical equation of state. At last, in ...
This simple model is the basis for the "law of the wall", which is a surprisingly accurate model for wall-bounded, attached (not separated) flow fields with small pressure gradients. More general turbulence models have evolved over time, with most modern turbulence models given by field equations similar to the Navier–Stokes equations .