Search results
Results from the WOW.Com Content Network
The law can be formulated mathematically in the fields of fluid mechanics and continuum mechanics, where the conservation of mass is usually expressed using the continuity equation, given in differential form as + =, where is the density (mass per unit volume), is the time, is the divergence, and is the flow velocity field.
The law is derived from the principles of conservation of mass and momentum of the air stream flowing through an idealized "actuator disk" that extracts energy from the wind stream. According to Betz's law, no wind turbine of any mechanism can capture more than 16/27 (59.3%) of the kinetic energy in wind.
The formula defines the energy E of a particle in its rest frame as the product of mass (m) with the speed of light squared (c 2). Because the speed of light is a large number in everyday units (approximately 300 000 km/s or 186 000 mi/s), the formula implies that a small amount of mass corresponds to an enormous amount of energy.
Strictly speaking the above equation holds also for systems with chemical reactions if the terms in the balance equation are taken to refer to total mass, i.e. the sum of all the chemical species of the system. In the absence of a chemical reaction the amount of any chemical species flowing in and out will be the same; this gives rise to an ...
A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity ...
In engineering and physics, g c is a unit conversion factor used to convert mass to force or vice versa. [1] It is defined as = In unit systems where force is a derived unit, like in SI units, g c is equal to 1.
For example, in the mass continuity equation for flowing water, if 1 gram per second of water is flowing through a pipe with cross-sectional area 1 cm 2, then the average mass flux j inside the pipe is (1 g/s) / cm 2, and its direction is along the pipe in the direction that the water is flowing. Outside the pipe, where there is no water, the ...
For typical applications in nuclear physics, where one particle's mass is much larger than the other the reduced mass can be approximated as the smaller mass of the system. The limit of the reduced mass formula as one mass goes to infinity is the smaller mass, thus this approximation is used to ease calculations, especially when the larger ...