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Concept
Mass flow rate
Summary
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 (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:
i.e., the flow of mass m through a surface per unit time t.
The overdot on the m 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 change in mass is the amount that flows after crossing the boundary for some time duration, not the initial amount of mass at the boundary minus the final amount at the boundary, since the change in mass flowing through the area would be zero for steady flow.
Mass flow rate can also be calculated by
where
or Q = volume flow rate,
ρ = mass density of the fluid,
v = flow velocity of the mass elements,
A = cross-sectional vector area/surface,
jm = mass flux.
The above equation is only true for a flat, plane area. In general, including cases where the area is curved, the equation becomes a surface integral:
The area required to calculate the mass flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface, e.g. for substances passing through a filter or a membrane, the real surface is the (generally curved) surface area of the filter, macroscopically - ignoring the area spanned by the holes in the filter/membrane. The spaces would be cross-sectional areas. For liquids passing through a pipe, the area is the cross-section of the pipe, at the section considered. The vector area is a combination of the magnitude of the area through which the mass passes through, A, and a unit vector normal to the area, . The relation is .
Official source
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