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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 x-axis is usually some function of compressor entry mass flow, usually corrected flow or non-dimensional flow, as opposed to real flow. This axis can be considered a rough measure of the axial Mach number of the flow through the device.
In a nozzle or other constriction, the discharge coefficient (also known as coefficient of discharge or efflux coefficient) is the ratio of the actual discharge to the ideal discharge, [1] i.e., the ratio of the mass flow rate at the discharge end of the nozzle to that of an ideal nozzle which expands an identical working fluid from the same initial conditions to the same exit pressures.
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 ...
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.
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 ...
If the gas is being released from a closed high-pressure vessel, the above steady state equations may be used to approximate the initial mass flow rate. Subsequently, the mass flow rate decreases during the discharge as the source vessel empties and the pressure in the vessel decreases. Calculating the flow rate versus time since the initiation ...
The correction for the velocity that is obtained from the second equation one has with incompressible flow, the non-divergence criterion or continuity equation ∇ ⋅ v = 0 {\displaystyle \nabla \cdot \mathbf {v} =0}