For a Newtonian fluid, the deviatoric stress tensor is related to the velocity by

For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier-Stokes equations, which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on velocity gradients and pressure.

For the case where the masses of two bodies are comparable, an exact Newtonian solution is still available, and qualitatively similar to the case of dissimilar masses, by centering the coordinate system on the center of mass of the two.

For example, Newtonian dynamics ( which is based on Galilean transformations ) is the low speed limit of special relativity ( since the Galilean transformation is the low-speed approximation to the Lorentz transformation ).

For this reason, these equations are usually written for Newtonian fluids.

For example, both Kepler's laws of the motion of the planets and Galileo's theories of motion worked out for terrestrial objects are reducible to Newtonian theories of mechanics, because all the explanatory power of the former are contained within the latter.

For example a Newtonian telescope of aperture is a moderately easy science fair project.

For example, Newtonian physics, general relativity and quantum mechanics are three distinct systems, each scientifically proven to have integrity according to their base assumptions and measures, but all three of which produce different extrapolated values when applied to real world situations.

For example, Maxwell's equations with material absorption or Newtonian mechanics with friction are not time-reversal invariant at the macroscopic level where they are normally applied, even if they are invariant at the microscopic level when one includes the atomic motions the " lost " energy is translated into.

For instance, in Newtonian mechanics, an observed acceleration can be explained by reference to an applied force.

For example, simplified climate models may use Newtonian cooling, instead of a full ( and computationally expensive ) radiation code, to maintain atmospheric temperatures.

For example, it was known in 1859 that the observed perihelion precession of Mercury violated Newtonian mechanics, but the theory remained the best explanation available until relativity was supported by sufficient evidence.

For most planets, the Newtonian model's predictions are accurate ; for Mercury, it is slightly inaccurate and the model of general relativity must be used instead.

For example, water is Newtonian, because it continues to exemplify fluid properties no matter how fast it is stirred or mixed.

For Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure ( and also the chemical composition of the fluid if the fluid is not a pure substance ), not on the forces acting upon it.

For instance, Newtonian physics admits solutions where particles accelerate continuously, heading out towards infinity.

For all Newtonian fluids in laminar flow the shear stress is proportional to the strain rate in the fluid where the viscosity is the constant of proportionality.

For the Newtonian fluid the slope of this line is the viscosity, which is the only parameter needed to describe its flow.

For a general discussion including mass in Newtonian mechanics, see the article on mass.

For example Newtonian mechanics, by modern standards, is factually incorrect, as it fails to take into account relativity or quantum mechanics, but it is still a valuable and valid approximation to those theories in many situations.

For a stationary, incompressible Newtonian fluid, these equations can be written in Einstein notation as:

For a constrained Newtonian dynamical system the constraints described by the equations () are usually implemented by some mechanical framework.

For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit ; equivalently, the LRL vector is said to be conserved.

For Newtonian liquids ( η ’

For example, it may go from having only periodic motions to apparently erratic behavior, as in the transition to turbulence of a fluid.

For most organisms, the resting period is a stage of preparation during which the secretion of fluid from the moulting glands of the epidermal layer and the loosening of the underpart of the cuticle occur.

For example, " brake fluid " is hydraulic oil and will not perform its required function if there is gas in it.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated.

For liquids, whether the incompressible assumption is valid depends on the fluid properties ( specifically the critical pressure and temperature of the fluid ) and the flow conditions ( how close to the critical pressure the actual flow pressure becomes ).

For an analogy, the supergravity description is like treating water as a continuous, incompressible fluid.

For example, the pasteurization standards for cream differ from the standards for fluid milk, and the standards for pasteurizing cheese are designed to preserve the phosphatase enzyme, which aids in cutting.

For a typical " pumping " configuration, the work is imparted on the fluid, and is thus positive.

For the fluid imparting the work on the pump ( i. e. a turbine ), the work is negative power required to drive the pump is determined by dividing the output power by the pump efficiency.

For example, singing " Happy Birthday " or other relatively common, repeated linguistic discourses could be fluid in people who stutter.

For instance, Institute investigators have found that as the heart beats, the syrinx fluid is abruptly forced downward.

For native peoples like the Māori in New Zealand, there is conflict between the fluid identity assumed as part of modern society and the traditional identity with the obligations that accompany it ; the loss of language heightens the feeling of isolation and damages the ability to perpetuate tradition.

For instance, the obsolete scientific theory that put forward an understanding of heat transfer in terms of the movement of caloric fluid was eliminated when a theory of heat as energy replaced it.

For example, the thermistor may be used as a flow rate sensor, since the dissipation constant increases with the rate of flow of a fluid past the thermistor.

For example, watermark fluid may be applied to the back of a stamp to temporarily reveal the watermark.

For limited applications, Computational fluid dynamics ( CFD ) can increase or possibly replace the use of wind tunnels.

Four versions of opium as a fluid extract were also offered: ( 1 ) Opium, Concentrated ( assayed ) " For making Tincture Opii ( Laudanum ) U. S. P.

For example, the spinning rotor may be suspended in a fluid, instead of being pivotally mounted in gimbals.

a toilet, call a plumber ; For equivalent fluid level control in a

For large Strouhal numbers ( order of 1 ), viscosity dominates fluid flow, resulting in a collective oscillating movement of the fluid " plug ".

For low values of the Reynolds number (< 1 ), which is true of most aerosol motion, Stokes ' law describes the force of resistance on a solid spherical particle in a fluid.