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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 ...
Defining equation SI units Dimension Flow velocity vector field u = (,) ... Mass current, mass flow rate: I m = / kg s −1 [M][T] −1: Mass current density j ...
Using ideal gas equation of state for constant temperature process (i.e., / is constant) and the conservation of mass flow rate (i.e., ˙ = is constant), the relation Qp = Q 1 p 1 = Q 2 p 2 can be obtained. Over a short section of the pipe, the gas flowing through the pipe can be assumed to be incompressible so that Poiseuille law can be used ...
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.
The flow rate can be converted to a mean flow velocity V by dividing by the wetted area of the flow (which equals the cross-sectional area of the pipe if the pipe is full of fluid). Pressure has dimensions of energy per unit volume, therefore the pressure drop between two points must be proportional to the dynamic pressure q.
In physics and engineering, mass flux is the rate of mass flow per unit of area. Its SI units are kg ⋅ s −1 ⋅ m −2. The common symbols are j, J, q, Q, φ, or Φ (Greek lowercase or capital Phi), sometimes with subscript m to indicate mass is the flowing quantity. This flux quantity is also known simply as "mass flow". [1] "
In turbulent flow the flow rate is proportional to the square root of the pressure gradient, as opposed to its direct proportionality to pressure gradient in laminar flow. Using the definition of the Reynolds number we can see that a large diameter with rapid flow, where the density of the blood is high, tends towards turbulence.
Some carbonate reservoirs have many fractures, and Darcy's equation for multiphase flow is generalized in order to govern both flow in fractures and flow in the matrix (i.e. the traditional porous rock). The irregular surface of the fracture walls and high flow rate in the fractures may justify the use of Forchheimer's equation.