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In general, electric potential is equivalent to hydraulic head. This model assumes that the water is flowing horizontally, so that the force of gravity can be ignored. In this case, electric potential is equivalent to pressure. The voltage (or voltage drop or potential difference) is a difference in pressure between two points.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
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The free Euler equations are conservative, in the sense they are equivalent to a conservation equation: + =, or simply in Einstein notation: + =, where the conservation quantity in this case is a vector, and is a flux matrix. This can be simply proved.
An illustrative example is the derivation of the boundary layer equations from the full Navier-Stokes equations governing fluid flow. In many cases, the asymptotic expansion is in power of a small parameter, ε : in the boundary layer case, this is the nondimensional ratio of the boundary layer thickness to a typical length scale of the problem.
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In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility [1] or, if the temperature is held constant, the isothermal compressibility [2]) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change.
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