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The product GM is the standard gravitational parameter and is often known to higher precision than G or M separately. The potential has units of energy per mass, e.g., J/kg in the MKS system. By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero.
For a water-filled glass tube in air at standard conditions for temperature and pressure, γ = 0.0728 N/m at 20 °C, ρ = 1000 kg/m 3, and g = 9.81 m/s 2. Because water spreads on clean glass, the effective equilibrium contact angle is approximately zero. [4] For these values, the height of the water column is
The variation formula computations above define the principal symbol of the mapping which sends a pseudo-Riemannian metric to its Riemann tensor, Ricci tensor, or scalar curvature.
For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
This equation permits the prediction of an unknown transfer coefficient when one of the other coefficients is known. The analogy is valid for fully developed turbulent flow in conduits with Re > 10000, 0.7 < Pr < 160, and tubes where L/d > 60 (the same constraints as the Sieder–Tate correlation). The wider range of data can be correlated by ...
In magnetohydrodynamics, the magnetic Reynolds number (R m) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by:
The table of the initial values of () (these values are also called the "figurate numbers for the n-dimensional cross polytopes" in the OEIS [6]) may illustrate the recursion formula (1), which can be taken to mean that each entry is the sum of the three neighboring entries: to its left, above and above left, e.g. () = = + +.
Magnetic hysteresis can be characterized in various ways. In general, the magnetic material is placed in a varying applied H field, as induced by an electromagnet, and the resulting magnetic flux density (B field) is measured, generally by the inductive electromotive force introduced on a pickup coil nearby the sample.