For the following formalism, the rotating frame of reference is regarded as a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame denoted the stationary frame.

For memoryless sources, this is merely the entropy of each symbol, while, in the case of a stationary stochastic process, it is

For the more general case of a process that is not necessarily stationary, the average rate is

For stationary sources, these two expressions give the same result.

For stationary and shaft engines including propeller engines, fuel consumption is measured by calculating the brake specific fuel consumption, which measures the mass flow rate of fuel consumption divided by the power produced.

For example, consider a stationary object in an inertial frame.

For example, a tree could be stationary with respect to an observer on earth, however it will be viewed as moving along with planet Earth for an observer in space.

For example, in a hypothetical stationary population in which half the population dies before the age of five, but everybody else dies at exactly 70 years old, the life expectancy at age zero will be about 37 years, while about 25 % of the population will be between the ages of 50 and 70.

For example, suppose there are two bodies of equal mass, one stationary and one approaching the other at a speed ( as in the figure ).

For example, a stationary projector in the front would have projected an image of a church courtyard while a moving projector from behind would project the image of the phantom The Bleeding Nun, an image which came from the novel The Monk by Matthew Gregory Lewis.

For the case of light alpha particles scattering off heavy nuclei, as in the experiment performed by Rutherford, the reduced mass is essentially the mass of the alpha particle and the nucleus off of which it scatters is essentially stationary in the lab frame.

For the rest of his life he wrote on black-bordered stationary.

For instance, the " use-before " date is often applied to products with this technique ; in this application the head is stationary and the product moves past.

For this reason, animals are regarded in general semantics as space-binders, and plants, which are usually stationary, as energy-binders.

For high-quality studio recording, all of these formats were effectively made obsolete in the early 1980s by two competing reel-to-reel formats with stationary heads: Sony's DASH format and Mitsubishi's continuation of the X-80 recorder, which was improved upon to become the ProDigi format.

For stationary applications, in particular MW-class installations, copper-brass constructions are still dominant.

For a single constraint, we use the statement above to say that at stationary points the direction that changes f is in the same direction

For this reason, one must either modify the formulation to ensure that it's a minimization problem ( for example, by extremizing the square of the gradient of the Lagrangian as below ), or else use an optimization technique that finds stationary points ( such as Newton's method without an extremum seeking line search ) and not necessarily extrema.

For example, in the laminar flow within a pipe with constant cross section, all particles travel parallel to the axis of the pipe ; but faster near that axis, and practically stationary next to the walls.

For continued signals that describe for example stationary physical processes, it makes more sense to define a power spectral density ( PSD ), which describes how the power of a signal or time series is distributed with frequency.

For the incline from Euston Station to Chalk Farm, Stephenson devised a system that would draw trains up the hill by a rope using a stationary steam engine near The Roundhouse.

For example, a typical stationary radiographic x-ray machine also includes an ion chamber and grid.

For example, a globally stably stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater.

** For many years, the crystal ball remained stationary on the table.

For a stationary moving deflagration front, these two timescales are equal: The heat generated by burning is equal to the heat carried away by heat transfer.

For incompressible flows, density remains constant.

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 incompressible flow, the divergence of the volume flux is zero.

For ships, unlike aircraft, one deals with incompressible flows, where change in water density is negligible ( a pressure rises close to 1000kPa leads to a change of only 2 – 3 kg / m < sup > 3 </ sup >).

For a flow to be incompressible the sum of these terms should be zero.

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 example, Shafranov used a magnetohydrodynamic ( MHD ) analogy to Hill's stationary fluid mechanical vortex to consider the equilibrium conditions of axially symmetric MHD configurations, reducing the problem to the theory of stationary flow of an incompressible fluid.

For instance, the Lens space contains an incompressible Klein bottle that is not-injective.

For example, it is common to treat seawater as incompressible.

For incompressible flow, the continuity equation and Navier-Stokes equations are filtered, yielding the filtered incompressible continuity equation,

For a homogeneous fluid and an incompressible flow, the flow velocities are split into a mean part and a fluctuating part using Reynolds decomposition:

For simplicity, consider an incompressible fluid:

For instance, for an incompressible, viscous, Newtonian fluid, the continuity and momentum equations — the incompressible Navier – Stokes equations — can be written as

For an incompressible material,.

For an incompressible Mooney – Rivlin material with

For an incompressible Mooney-Rivlin material,

For the case of an incompressible Mooney – Rivlin material under uniaxial elongation, and.