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Potential flow in two dimensions is simple to analyze using conformal mapping, by the use of transformations of the complex plane. However, use of complex numbers is not required, as for example in the classical analysis of fluid flow past a cylinder. It is not possible to solve a potential flow using complex numbers in three dimensions. [11]
The problem of potential compressible flow over circular cylinder was first studied by O. Janzen in 1913 [4] and by Lord Rayleigh in 1916 [5] with small compressibility effects. Here, the small parameter is the square of the Mach number M 2 = U 2 / c 2 ≪ 1 {\displaystyle \mathrm {M} ^{2}=U^{2}/c^{2}\ll 1} , where c is the speed of sound .
In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux .
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, density, speed and height. Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum. [1]:
ϕ is known as a velocity potential for u. A velocity potential is not unique. If ϕ is a velocity potential, then ϕ + f(t) is also a velocity potential for u, where f(t) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable.
Water potential is the potential energy of water per unit volume relative to pure water in reference conditions. Water potential quantifies the tendency of water to move from one area to another due to osmosis , gravity , mechanical pressure and matrix effects such as capillary action (which is caused by surface tension ).
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.
Developmental bioelectricity is a sub-discipline of biology, related to, but distinct from, neurophysiology and bioelectromagnetics.Developmental bioelectricity refers to the endogenous ion fluxes, transmembrane and transepithelial voltage gradients, and electric currents and fields produced and sustained in living cells and tissues.