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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.
Both gas and liquid flow can be measured in physical quantities of kind volumetric flow rate or mass flow rates, with respective SI units such as cubic meters per second or kilograms per second, respectively. These measurements are related by the material's density. The density of a liquid is almost independent of conditions.
[1] [2] [3] At choked flow, the mass flow rate can be increased only by increasing the upstream density of the substance. The choked flow of gases is useful in many engineering applications because the mass flow rate is independent of the downstream pressure, and depends only on the temperature and pressure and hence the density of the gas on ...
A flow that is not a function of time is called steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow is known as unsteady (also called transient [8]). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference.
Schematic view of an SPH convolution Flow around cylinder with free surface modelled with SPH. See [1] for similar simulations.. Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.
Density meters have many applications in various parts of various industries. Density meters are used to measure slurries, sludges, and other liquids that flow through the pipeline. Industries such as mining, dredging, wastewater treatment, paper, oil, and gas all have uses for density meters at various points during their respective processes.
Elutriation is a process for separating particles based on their size, shape and density, using a stream of gas or liquid flowing in a direction usually opposite to the direction of sedimentation. This method is mainly used for particles smaller than 1 μm.
A change in the density over time would imply that the fluid had either compressed or expanded (or that the mass contained in our constant volume, dV, had changed), which we have prohibited. We must then require that the material derivative of the density vanishes, and equivalently (for non-zero density) so must the divergence of the flow velocity: