Velocity instantaneous speed

The compulsory fulfillment of conditions (4.2) and (4.3) physically follows from the fact that a one-dimensional Markov process is nondifferentiable that is, the derivative of Markov process has an infinite variance (instantaneous speed is an infinitely high). However, the particle with the probability equals unity drifts for the finite time to the finite distance. That is why the particle velocity changes its sign during the time, and the motion occurs in an opposite directions. If the particle is located at some finite distance from the boundary, it cannot reach the boundary in a trice—the condition (4.2). On the contrary, if the particle is located near a boundary, then it necessarily crosses the boundary— the condition (4.3). 

To better understand the difference between the aver speed and the instantaneous speed, ask yourself the following question. If you needed to locate the car, would you be able to locate the car knowing just the average speed of the cai The knowlet of the average speed of the car would not be sufficient. To know where the car is at all times, you need more information, such as the instantaneous speed of the car and the direction in which it is traveling. This means you must know the instantaneous velodly of the car. Note that when we say velocity of a car, we not only refer to the speed of the car but also the direction in which it moves. 

Example 10 Response to Instantaneous Valve Closing Compute the wave speed and maximum pressure rise for instantaneous valve closing, with an initial velocity of 2,0 m/s, in a 4-in Schedule 40 steel pipe with elastic modulus 207 X 10 Pa, Repeat for a plastic pipe of the same dimensions, with E = 1.4 X 10 Pa. The liquid is water with P = 2.2 X 10 Pa and p = 1,000 kg/m. For the steel pipe, D = 102,3 mm, b = 6,02 mm, and the wave speed is... 

The terms rate, speed, and velocity are all synonymous in chemical kinetics, though this is not so in mechanics. It takes different periods of time to complete different reactions. The neutralization reaction between acids and bases, mentioned earlier as an example of homogeneous reactions, takes place almost instantaneously at room temperature and under atmospheric pressure. However, it takes many days for iron to rust under these conditions. Thus, the rates of reactions that may take place under the same conditions of temperature and pressure may differ very significantly. When carbon or sulfur or phosphorus bums in... 

Fig. 4.3.3 (a) Shear flow of a Newtonian fluid defined as the ratio of the shear stress and trapped between the two plates (each with a shear rate, (b) A polymeric material is being large area of A). The shear stress (a) is defined stretched at both ends at a speed of v. The as F/A, while the shear rate (y) is the velocity material has an initial length of L0 and an gradient, dvx/dy. The shear viscosity (r s) is (instantaneous) cross-sectional area of A. 

Measurement of the velocity of a large particle. The investigation of the turbulence characteristics in the liquid phase of a bubbly flow has generated detailed studies on the use of thermal anemometry and optical anemometry in gas-liquid two-phase flows. These techniques have been proved to be accurate and reliable for the measurement of the instantaneous liquid velocity in bubble flow. However, the velocity of the gas bubbles—or, more precisely, the speed of displacement of the gas-liquid interfaces—is still an active research area. Three techniques that have been proposed to achieve such measurement were reviewed by Delhaye (1986), as discussed in the following paragraphs. 

The contradiction is only an apparent one, and the difference between the theories lies in the hypotheses. The measurement of the speeds of reaction depends upon the conditions of the experiment. If the reaction between two components of reaction actually takes place instantaneously, we can vary the time of reaction entirely at will by the period of time during which we add one of the components. If the latter is used up with immeasurable rapidity, the measured velocity of reaction must naturally always remain proportional to the added quantity of the reaction components. The Nernst theory is based on relations in which this subsequent delivery is effected only by the diffusion, the reacting agent furnished by the current being... 

This behaviour assumes that the environment is instantaneously available within the craze and clearly at high speeds this will not be so. The limiting factor wili be the flow of the fluid within the ctsae and we would expect a transition from the lowar to the upper line as crack speed increases. An estimate of the effect may be imde by assuming that the flow is governed by D Arcy s Law for flow in porous media such that the flow velocity, V, is given by ... 

Linear profiles are the simplest profiles to use for powder compressions. Typically, a sawtooth or v-shaped profile is used where the punch is extended at a constant velocity and retracts at a constant velocity. In theory, during a sawtooth profile, the punch reverses its motion instantaneously between the compression and a decompression strokes. At low speeds (e.g.. <1 mm/sec), the hydraulic response system can easily accommodate this discontinuity. However, at high speeds (>100mm/.sec), the control system may show a small lag in the position-time waveform (<10 milliseconds) as it attempts to rapidly reverse the direction of punch. The sawtooth waveform is commonly used for more fundamental compression studies (e.g.. Heckel analysis), where the desired powder volume reduction is proportional to time. It is also u.seful when evaluating instrument performance during factory acceptance testing. 

---