Instantaneous acceleration

The self-similar solution is an asymptotic solution that develops when t/r - m, with r as the characteristic time of the condensation process. This development is studied numerically for a mixture of nitrogen gas and water vapour. At t = 0, a piston is accelerated instantaneously to a constant velocity, causing a one-dimensional unsteady rarefaction wave in a nadxture of gas and vapour. The wave is travelling to the left and the wave front runs with x/aQt = -1. A simple relaxation model is assumed ... 

The operation of system valves (also starting and shutdown of pumps) has a significant effect on the transient fluid pressures in the piping system because of the acceleration and deceleration of the fluid as it changes its velocity. As a simple example, the maximum head rise caused by the instantaneous closing of a valve is given by... 

Equation (2.1) for the motor vehicle implies that when there is a change in accelerator angle, there is an instantaneous change in vehicle forward speed. As all car drivers know, it takes time to build up to the new forward speed, so to model the dynamic characteristics of the vehicle accurately, this needs to be taken into account. 

When applying Newton s law to a moving automobile, acceleration depends on the excess of power over that required for constant-speed driving, namely P -P,.. From this it follows that the instantaneous acceleration (a) of the vehicle at a given road speed (V) is... 

Acceleration. A measure of the instantaneous rate of change in velocity with respect to time. Acceleration is a vector quantity. 

When looking for the velocities of points on a rigid body, the method of instantaneous centers can often be used. If the velocity of two points on the body are known, those points and all other points on the body can be considered to be rotating with the same angular velocity about some motionless central point. This central point is called the instantaneous center of zero velocity. The instantaneous center generally moves through space as a function of time and has acceleration. It does not represent a point about which acceleration may be determined. 

In Figure 2-16 a 10 lb cylinder with a 3-in. radius rolls down a 30° incline. What is its angular acceleration and the linear acceleration of its center of mass In the free-body diagram of Figure 2-16, the point of contact between the wheel and the ramp is the instantaneous center of zero velocity. Thus,... 

In reciprocators hf is calculated at peak instantaneous flow, including maximum loss through a dirty filter, and an additional head loss to allow for pulsation acceleration is used ... 

The reaction velocity is comparatively slow, but increases with increasing concentration of acid. The addition of three drops of a neutral 20 per cent ammonium molybdate solution renders the reaction almost instantaneous, but as it also accelerates the atmospheric oxidation of the hydriodic acid, the titration is best conducted in an inert atmosphere (nitrogen or carbon dioxide). 

This observation immediately rules out the possibility that NEMCA is an electrocatalytic phenomenon causing only a local acceleration of the catalytic rate at the three-phase-boundaries (tpb) metal-solid electrolyte-gas. In such a case the rate increase would obviously be instantaneous during a galvanostatic transient. 

Upon injection of CD into the reactor during racemic hydrogenation the rate acceleration was always instantaneous, while the optical yield vs conversion dependencies showed a monotonic increase type behaviour as seen in Figure 7. In acetic acid the increase part of the above dependence is so fast that it hardly can be followed by our sampling technique. At low concentration of modifier the optical yield passes through a maximum In this case the... 

Continuous ion sources, such as ESI, can be connected to the TOF analyzers through orthogonal acceleration (oa-TOF) [205-209]. In oa-TOF, the ions generated by the source enter the TOF analyzer perpendicular to its main axis (Fig. 2.11). The acceleration potential is initially set to zero and the start pulse is generated instantaneously as the potential is raised and the ions are accelerated into the field-free flight tube. 

Interestingly, the shape of the wake is similar to that developed behind a hypersonic blunt body where the flow converges to form a narrow recompression neck region several body diameters downstream of the rear stagnation point due to strong lateral pressure gradients. The liquid material, that is continuously stripped off from the droplet surface, is accelerated almost instantaneously to the particle velocity behind the wave front and follows the streamline pattern of the wake, suggesting that the droplet is reduced to a fine micromist. 

As discussed above, the GLM was developed in the spirit of Reynolds-stress modeling. An obvious extension is to devise large-eddy-based closures for the conditional acceleration. For this case, it is natural to decompose the instantaneous velocity into its resolved and unresolved components 42... 

Since we could not prepare a stable solution of the ester, we attempted its preparation in the styrene solution to be polymerised. Silver perchlorate was dissolved in this and the reaction was started by the crushing of a phial containing 1-phenylethyl bromide (under our conditions styrene was not polymerised by the silver perchlorate alone). The solutions became cloudy because of the formation of colloidal silver bromide, but no colour formation could be observed until the end of the polymerisation then the solutions became yellow, very like the reaction mixtures in which perchloric acid had been used as catalyst. The ester was found to be as effective a catalyst as anhydrous perchloric acid. Equal concentrations of the ester and the acid produced very similar polymerisations as shown in the Figure. The accelerating parts of the curves obtained with the ester as catalyst are readily explained by the fact that the reaction between silver perchlorate and 1-phenylethyl bromide is not instantaneous and therefore a steady increase in catalyst concentration characterises the first part of the polymerisation. 

The first term of Eq. (11-11) is the Stokes drag for steady motion at the instantaneous velocity. The second term is the added mass or virtual mass contribution which arises because acceleration of the particle requires acceleration of the fluid. The volume of the added mass of fluid is 0.5 F, the same as obtained from potential flow theory. In general, the instantaneous drag depends not only on the instantaneous velocities and accelerations, but also on conditions which prevailed during development of the flow. The final term in Eq. (11-11) includes the Basset history integral, in which past acceleration is included, weighted as t — 5) , where (t — s) is the time elapsed since the past acceleration. The form of the history integral results from diffusion of vorticity from the particle. 

The first term again represents drag in steady motion at the instantaneous velocity, with Cd an empirical function of Re as in Chapter 5. The other terms represent contributions from added mass and history, with empirical coefficients, Aa and Ah, to account for differences from creeping flow. From measurements of the drag on a sphere executing simple harmonic motion in a liquid, Aa and Ah appeared to depend only on the acceleration modulus according to ... 

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