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In most contexts a mention of rate of fluid flow is likely to refer to the volumetric rate. In hydrometry, the volumetric flow rate is known as discharge. Volumetric flow rate should not be confused with volumetric flux, as defined by Darcy's law and represented by the symbol q, with units of m 3 /(m 2 ·s), that is, m·s −1. The integration ...
Thus the rate of heat flow into V is also given by the surface integral () = () where n(x) is the outward pointing normal vector at x. The Fourier law states that heat energy flow has the following linear dependence on the temperature gradient H ( x ) = − A ( x ) ⋅ ∇ u ( x ) {\displaystyle \mathbf {H} (x)=-\mathbf {A} (x)\cdot \nabla u(x ...
Flow velocity vector field u = ... mass flow rate: I m = / kg s −1 [M][T] −1: Mass current density ... The Cambridge Handbook of Physics Formulas. Cambridge ...
It is very common in many fields, including engineering, physics and the study of differential equations, to use a notation that makes the flow implicit.Thus, x(t) is written for (), and one might say that the variable x depends on the time t and the initial condition x = x 0.
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 ...
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]
It describes the relationship between the pressure drop across an orifice valve or other assembly and the corresponding flow rate. Mathematically the flow coefficient C v (or flow-capacity rating of valve) can be expressed as =, where Q is the rate of flow (expressed in US gallons per minute), SG is the specific gravity of the fluid (for water ...
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.