Proper velocity Proper velocity In relativity, proper velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object. Proper velocity equals velocity at low speeds. Proper velocity at high speeds, moreover, retains many of the properties that velocity loses in relativity compared with Newtonian theory. For example, proper velocity equals momentum per unit mass at any speed, and therefore
Mass flow rate 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, v, with the following relationship: The quantity can be used in particle Reynolds number or mass transfer coefficient calculation for fixed and fluidized bed systems. 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