Characteristic speed

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Coupling selection is highly dependent on the mode of operation, which includes torsional characteristics, speed, and the operating envelope. 

Equation (52) allows us to estimate the impact of viscoelastic braking on the capillary flow rate. As an example, we will consider that the liquid is tricresyl phosphate (TCP, 7 = 50 mN-m t = 0.07 Pa-s). The viscoelastic material is assumed to have elastic and viscoelastic properties similar to RTV 615 (General Electric, silicone rubber), i.e., a shear modulus of 0.7 MPa (E = 2.1 MPa), a cutoff length of 20 nm, and a characteristic speed, Uo, of 0.8 mm-s [30]. TCP has a contact angle at equilibrium of 47° on this rubber. 

Dressed ions carry electrons while slowing down. This feature is important for all ions below some characteristic speed A rough estimate for Vc is... 

FIGURE 3.5 Sound waves in air are waves of gas pressure. The positions of the maxima and minima change with time. The waves travel at a characteristic speed s = kv determined by properties of the air molecules and independent of wavelength or frequency. 

Another quantity which is closely related to the average molecular speed is the speed of sound, which we will write as 5SOund- As noted in Chapter 3, sound waves are actually waves of gas pressure (Figure 3.6)—the density of gas molecules is alternately slightly higher or lower than the equilibrium value. This disturbance travels at a characteristic speed which is clearly not very different from the average molecular speed, but getting the precise numerical value requires a fairly sophisticated treatment. The answer turns out to be... 

The accompanying chart shows the low limits practicable for specific or characteristic speed at various heads. If speeds are made lower, the runner passages become very long and narrow, the diameter great and the cost high. 

Fig 33.—Relations between characteristic speed, efficiency and gate-age of reaction turbines. 

In a coaxial mixer, the selection of the characteristic speed and dimension that appear in the expression of these dimensionless numbers is ambiguous, as we have... 

B16. Buller, A. J., Eccles, J. C., and Eccles, R. M., Interactions between motoneurones and muscles in respect of the characteristic speeds of their responses. J. Physiol. (London) 160, 417-439 (1960). 

The mean size of the droplets formed by shearing can be approximated by equating an estimated shear stress r in the system, given by the characteristic speed divided by the characteristic length L over which the liquid is sheared (e.g. the radius of the container) r juulL, with an estimated interfacial restoring pressure py yir. The radius r of the tightest curvature that can be created with shear rcan be then estimated from r = py, which yields ... 

Velocity of surface active material Molar average velocity, Eq. (2.4.7) Bubble interface speed Characteristic speed Electroosmotic velocity past a plane surface... 

Let us rewrite the system, Eqs. (3.5.1) to (3.5.4), in terms of reduced dimensionless variables, recognizing that the choice of characteristic scales is to some extent an arbitrary one. With L, U, and t, respectively, the characteristic length, characteristic speed, and characteristic time of the problem, and with asterisks denoting a reduced dimensionless variable, we have... 

This line is termed a characteristic, which is a line in the x-t plane on which an ordinary differential equation may be written, in this case dp = 0. From Eqs. (5.4.19), (5.4.20), and the mass conservation relation dpidt = -djidx, it follows that the slope of the upward-propagating characteristic curve, or characteristic speed, is... 

This equation defines the characteristic speed, that is, the kinematic wave speed. Note that for s = constant the characteristic speed drldt= which is analogous to the wave speed in the gravity sedimentation problem except that here is not constant with distance. The analogy also holds with s — s p) if s d sp)/dp is defined as a hindered settling factor G(d>) (Eq. 5.4.18). 

As the Brenner-Cox (B27, C17) relations are not readily susceptible to further generalization it is appropriate to summarize them in some detail here. A nondimensional form is most convenient. As usual, let U be the velocity of any point O affixed to the body and the angular velocity of the body. Further, let a be any characteristic particle dimension and "f be any characteristic speed, e.g., U or a . The ultimate results are independent of the choice of these characteristic parameters. 7 = af pjn denotes the particle Reynolds number. A dimensionless hydrodynamic force and torque about O are defined as follows ... 

When FTIR spectrometers first appeared in the marketplace, they were bulky, expensive (> 100,000), and required frequent mechanical adjustments. For these reasons, their use was limited lu special applications where Iheir unique characteristics (speed, high resolution, sensilivily. and unparalleled wavelength precision and accuracy) were esscnlial. FT insiru-... 

The characteristic speed for bubble aspiration, Nq, is obtained from Eq. 14.3.g-3 ... 

Figure 5 shows a block diagram of GC-analysis. The gas, which has to be analysed, is transported by means of a carrier gas (in general Hehum) to the pre-cut coluttm, containing the prechosen stationary liquid phase. An equihbrium state is achieved between stationary and mobile phase, so that according to the different partitions of the pure substances in the mixture characteristic speeds of migration can be detected. 

A form of energy that has wave characteristics and that propa tes through a vacuum at the characteristic speed of 3.00 X 10 m/s. (Section 6.1)... 

The Euler equations (12), (13) can be shown [[iC to be strictly hyperbolic with the characteristic speeds given by... 

The earth manifests its presence in the solar wind in a manner analogous to that of a supersonic airplane traversing the atmosphere. Since the solar wind velocity is faster than the characteristic speed in the ionized gas, a shock wave (the bow shock) is established. The average location of the shock is some 10-14 earth radii outward on the sunward side (Fig. 3). On the earthward side of the shock wave is a region of more turbulent solar wind flow, the magnetosheath. Then, at an average altitude above the earth of some nine earth radii, the magnetopause exists... 

Deposit a small drop of octane on very clean glass and record the radius R,(t) as a function of time (see Fig. 1.17). Plot Tl t) on log/log paper. Check that TZ t, where a 0.1. If we replace the octane with a silicone oil, or even water, provided only that it can wet the glass, we find that all these liquids spread according to a universal law which does not depend on the liquid. If V = 7/ 7 is the characteristic speed and 17 the volume deposited, it is found that... 

Molecular weight Viscosity Density Surface tension Laplace length Characteristic speed Refractive index... 

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