Mass flow rate

In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is formula_1 (ṁ, pronounced "m-dot"), although sometimes "μ" (Greek lowercase mu) is used.
Sometimes, mass flow rate is termed "mass flux" or "mass current", see for example "Schaum's Outline of Fluid Mechanics". In this article, the (more intuitive) definition is used.
Mass flow rate is defined by the limit:
The reason for the dot product is as follows. The only mass flowing "through" the cross-section is the amount normal to the area, i.e. parallel to the unit normal. This amount is: 
where "θ" is the angle between the unit normal formula_4 and the velocity of mass elements. The amount passing through the cross-section is reduced by the factor formula_5, as "θ" increases less mass passes through. All mass which passes in tangential directions to the area, that is perpendicular to the unit normal, "doesn't" actually pass "through" the area, so the mass passing through the area is zero. This occurs when "θ" = "π"/2:
These results are equivalent to the equation containing the dot product. Sometimes these equations are used to define the mass flow rate.
Considering flow through porous media, a special quantity, superficial mass flow rate, can be introduced. It is related with superficial velocity, "vs", with the following relationship:
The quantity can be used in particle Reynolds number or mass transfer coefficient calculation for fixed and fluidized bed systems.
Usage.
In the elementary form of the continuity equation for mass, in hydrodynamics:
In elementary classical mechanics, mass flow rate is encountered when dealing with objects of variable mass, such as a rocket ejecting spent fuel. Often, descriptions of such objects erroneously invoke Newton's second law F =d("m"v)/d"t" by treating both the mass "m" and the velocity v as time-dependent and then applying the derivative product rule. A correct description of such an object requires the application of Newton's second law to the entire, constant-mass system consisting of both the object and its ejected mass.
Mass flow rate can be used to calculate the energy flow rate of a fluid:
where:
Energy flow rate has SI units of kilojoule per second or kilowatt.
Analogous quantities.
In hydrodynamics, mass flow rate is the rate of flow of mass. In electricity, the rate of flow of charge is electric current.