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 a Newtonian fluid these take the respective forms

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 a given pressure, different liquids boil at different temperatures.

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 many processes in the medical, pharmaceutical, military and general industries this is an advantage over inline sensors that may contaminate the liquids inside a vessel or tube.

For two-phase systems ( e. g., two liquid phases ), the vapor pressure of the system is the sum of the vapor pressures of the two liquids.

For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart.

For example, the transmission medium for sound received by the ears is usually air, but solids and liquids may also act as transmission media for sound.

For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used.

For unpackaged goods and liquids weigh stations confirm weight after loading and before delivery.

For liquids, the volumetric heat capacity is narrower: in the range 1. 3 to 1. 9 MJ / m³K.

For condensed phases ( solids and liquids ), the pressure dependence of solubility is typically weak and usually neglected in practice.

For offerings of liquids ( beverages ) by pouring, the term libation is used.

For submicrometre particle sizes, capillaries with diameters in the range of 0. 1 to 1 micrometres develop pressures in the range of to for silicate liquids and in the range of to for a metal such as liquid cobalt.

For homogenous liquids such as water, increased accuracy has been achieved through the inclusion of polarizability.

For liquids, various units are used depending upon the application and industry, but might include gallons ( U. S. liquid or imperial ) per minute, liters per second, bushels per minute or, when describing river flows, cumecs ( cubic metres per second ) or acre-feet per day.

For more objects, floating and sunken, and in gases as well as liquids ( i. e. a fluid ), Archimedes ' principle may be stated thus in terms of forces:

For instance, they determine the physical properties of liquids, the solubility of solids, and the organization of molecules in biological membranes.

For many liquids, dissolved oxygen can act as a quenching agent and lead to reduced light output, hence the necessity to seal the solution in an oxygen-free, air-tight enclosure.

For some substances, such as carbon and arsenical, sublimation is much easier than evaporation from the melt, because the pressure of their triple point is very high, and it is difficult to obtain them as liquids.

For liquids, transmittance is related to absorbance A ( not to be confused with absorptance ) as

For liquids e is replaced by 10.

For water and other liquids, this integral can be simplified significantly for many practical applications, based on the following two assumptions: Since many liquids can be considered incompressible, a reasonably good estimation can be made from assuming a constant density throughout the liquid.

For liquids and gases, typical frequency shifts are of the order of 1 – 10 GHz ( wavelength shifts of ~ 1 – 10 pm for visible light ).

For non-symmetric media ( e. g. liquids ), this induced change of susceptibility produces a change in refractive index in the direction of the electric field:

For example, there might be changes in shape or form ( for instance, liquids are reshaped as they are transferred from one vessel to another, humans change in their characteristics as they grow older ), in size ( e. g., a series of coins on a table might be placed close to each other or far apart ) in placement or location in space and time ( e. g., various objects or persons might be found at one place at one time and at a different place at another time ).