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An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
The above equation describes the Earth's gravitational potential, not the geoid itself, at location ,,, the co-ordinate being the geocentric radius, i.e., distance from the Earth's centre. The geoid is a particular equipotential surface, [ 27 ] and is somewhat involved to compute.
The velocity satisfies the continuity equation for incompressible flow: ∇ ⋅ u = 0. {\displaystyle \quad \nabla \cdot \mathbf {u} =0.} Although in principle the stream function doesn't require the use of a particular coordinate system, for convenience the description presented here uses a right-handed Cartesian coordinate system with ...
The method consists of filling the flow area with stream and equipotential lines, which are everywhere perpendicular to each other, making a curvilinear grid.Typically there are two surfaces (boundaries) which are at constant values of potential or hydraulic head (upstream and downstream ends), and the other surfaces are no-flow boundaries (i.e., impermeable; for example the bottom of the dam ...
This equation is valid provided ... Lines of constant ψ are known as streamlines and lines of constant φ are known as equipotential lines (see equipotential surface).
The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa 2 ·E, by Gauss's law equals πa 2 ·σ/ε 0. Thus, σ = ε 0 E . In problems involving conductors set at known potentials, the potential away from them is obtained by solving Laplace's equation , either analytically or ...
Isoclines are used to solve ordinary differential equations. In interpreting radar images, an isodop is a line of equal Doppler velocity, and an isoecho is a line of equal radar reflectivity. In the case of hybrid contours, energies of hybrid orbitals and the energies of pure atomic orbitals are plotted. The graph obtained is called hybrid contour.
The second lemniscate of the Mandelbrot set is a Cassini oval defined by the equation = {: (+) =}. Its foci are at the points c on the complex plane that have orbits where every second value of z is equal to zero, which are the values 0 and −1.