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In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of ordinary differential equations. Informally, a flow may be viewed as a continuous motion of points over time.
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.
For this reason flux represents physically a flow per unit area. ... mass flow rate: I m = / kg s −1 [M][T] −1: Mass current density ... The Cambridge Handbook of ...
The volume rate of flow of liquid through a source or sink (with the flow through a sink given a negative sign) is equal to the divergence of the velocity field at the pipe mouth, so adding up (integrating) the divergence of the liquid throughout the volume enclosed by S equals the volume rate of flux through S. This is the divergence theorem. [2]
Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid. It is a real vector that changes with space and time. Probability currents are analogous to mass currents in hydrodynamics and electric currents in electromagnetism .
Rate of flow may refer to: Mass flow rate, the movement of mass per time; Volumetric flow rate, the volume of a fluid which passes through a given surface per unit of ...
Diffusion flux, the rate of movement of molecules across a unit area (mol·m −2 ·s −1). (Fick's law of diffusion) [7] Volumetric flux, the rate of volume flow across a unit area (m 3 ·m −2 ·s −1). (Darcy's law of groundwater flow) Mass flux, the rate of mass flow across a unit area (kg·m −2 ·s −1). (Either an alternate form of ...
For a compressible fluid in a tube the volumetric flow rate Q(x) and the axial velocity are not constant along the tube; but the mass flow rate is constant along the tube length. The volumetric flow rate is usually expressed at the outlet pressure. As fluid is compressed or expanded, work is done and the fluid is heated or cooled.