Unit of velocity

Coordinates of atoms can be set by normal translation or rotation of HyperChem molecules. To set initial velocities, however, it is necessary to edit the HIN file explicitly. The unit of velocity in the HIN file is Angstroms/picosecond. Areact.hin file and a script react.scr are included with HyperChem to illustrate one simple reacting trajectory. In order to have these initial velocities used in a trajectory the Restart check box of the Molecular Dynamics Options dialog box must be checked. If it is not, the initial velocities in the HIN file will be ignored and a re-equilibration to the temperature T of the Molecular Dynamics Options dialog box will occur. This destroys any imposed initial conditions on the molecular dynamics trajectory. 

The permeability factor, K, has units of velocity and is inversely proportional to the viscosity of the gas. A permeabihty test is mn by passing air... 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

The problem with the SI base unit being a kilogram is the kilo part. The philosophical idea behind the SI system says any parameter (physical, chemical, mechanical, etc.) can be derived from a suitable combination of the others. For example, the SI unit of velocity is metres per second (m s-1), which is made up of the two SI fundamental units of length (the metre) and time (the second). A few of these combinations are cited in Table 1.3. 

A depth gauge uses a unit of length such as feet or meters a speed gauge uses a unit of velocity such as miles per hour (mph) or kilometers per hour (kph) the RPM gauge measures revolutions per minute. 

All secondary units must be coherent with the basic units (Table 1), e.g., the measuring unit of velocity must not be miles/hr or km/hr but m/sec. 

Under the steady-state conditions that usually apply (see p. 449), the rate of increase of product will be the same as the rate of decrease of substrate. The units of velocity are moles per liter per second (M s 1) or more traditionally in enzymology moles per liter per minute. We are interested in the instantaneous velocity, which at... 

The charge mobility has units of velocity divided by electric field, m2 V 1 s 1 (see Table 1.3 for values of the mobility of several ions in aqueous solution and [52] for the case of nonaqueous solutions). By inserting Eq. (1.135) into Eq. (1.134), one obtains... 

This expression yields an empirical parameter with units of velocity (cm s-1) which are independent of atmospheric concentration. Vg may be calculated on the basis of exposed leaf area, in the case of spaced plants, or in terms of the horizontal surface area for continuous swards such as cereal or grass crops. Both soil and plant are potentially available for contamination and the total velocity of deposition to a canopy can then be defined as... 

The detection of pressure drop across a restriction is undoubtedly the most widely used method of industrial flow measurement. If the density is constant, the pressure drop can be interpreted as a reading of the flow. In larger pipes or ducts, the yearly energy operating cost of differential-pressure (d/p)-type flowmeters can exceed the purchase price of the meter. The permanent pressure loss through a flowmeter is usually expressed in units of velocity heads, v2/2 g, where v is the flowing velocity, and g is the gravitational acceleration (9.819 m/s2, or 32.215 ft/s2, at 60° latitude). 

The term y/r/p0 is identified as having the units of velocity and is usually called the drag velocity. If v denotes this velocity, then v = y/T/po-We see, therefore, from the above equation that average velocity measurements at two given heights suffice to determine v. We shall have more to say in this connection when we consider sand storms. 

The permeability coefficient (k) has the units of velocity, that is, distance/time. It is determined either in laboratory experiments or derived from pumping tests. Both methods are semiquantitative, but are still highly informative, as the values observed for common rocks span more than seven orders of magnitude. A variety of units are in use—m/day being a common one. The following are a few of the average permeability or hydraulic conductivity values floating around in the literature, expressed in m/day ... 

Vtot in the above equation is a mass transfer velocity across the air-water interface. It has units of velocity (usually cm/s), and it is made up of two parts (a) the velocity of the compound through the boundary layer in the water to the interface (denoted by vw) and (b) the velocity of the compound through the boundary layer in the air as it leaves the air-water interface (denoted by va). The total mass transfer velocity is given by... 

Velocity is defined to be the rate at which the displacement of an object is changing as time changes. The basic unit of velocity, as of speed, is meters per second. Another common unit is kilometers per hour. If an object is traveling at a constant speed of v meters/second for t seconds and covers d meters, then the formulas connecting these quantities are... 

By dividing J by c0, a term having the units of velocity results. This function vD is called the diffusion velocity, defined as... 

In Equation 2.26, Jyw is the volume flow of water per unit area of the barrier per unit time. It can have units of m3 m-2 s 1, or m s 1, which are the units of velocity. 

The proportionality constant ki has units of velocity. The mechanical step is assumed to remove only the reacted material at a rate proportional to the fraction of the surface that has been reacted ... 

To compensate for experimental variations in E, the electrophoretic mobility of a particle has been defined as a fundamental characteristic of a molecule under given conditions of support medium, pH, ionic strength, and temperature. The electrophoretic mobility, p, usually reported in units of velocity per unit field strength, is given by Eq. 9.3 ... 

Figure 10. Test of scaling prediction made implicitly in Eq. (28). Experimental data for different temperatures between 53 and 373 K were taken from Ref. 80. The upper inset shows the maximum friction force as a function of temperature. The lower inset shows significantly worse scaling for linear creep, using ln(t)/T). The units of velocity are nanometers per second, and temperature is in degrees kelvin. With permission from Ref. 87. PItys. Rev. Lett. 87, 174301 (2001).

Primary and Secondary (Derived) Quantities Dimensional Constants A distinction is made between primary or base quantities and secondary quantities derived from them. The base quantities are based on standards and are quantified by comparison with them. The secondary quantities are derived from the primary ones according to physical laws, e.g. velocity = length/time. All secondary measuring units must be coherent with the base units, e.g. the measuring unit of velocity must not be miles/hr or km/hr but m/s ... 

We have carried out all of the analysis of this section with the equations and boundary conditions in dimensional form. However, in view of the rather large number of dimensional parameters that appear in (12-82)-(12-85), there is a definite advantage in nondimension-alizing. The problem is to choose characteristic scales because these must be intrinsic, and formed from the available dimensional parameters, rather than explicitly evident, The available parameters are p. p2. m, m, g, and y. Given that the mechanism for motion is the body force that is due to gravity, it would be surprising if the characteristic velocity did not involve g. In fact, a combination of dimensional parameters with units of velocity is (gv)1/3. The decision to use v or v2 in this definition is completely arbitrary. Hence we take... 

Another beautiful result is the general first order solution of the Gross-mann equation. We will choose the velocity c as our unit of velocity and obtain... 

The contraction coefficient, Kc , which has units of velocity heads, is given in Table 4.2. 

In atomic units, based on el, and m (or alternatively el,m and 47reo) as basic quantities, the unit of velocity (or 4 ) results automat-... 

What controls relativistic effects is actually not the ratio between the atomic unit of velocity and c, but rather that between a characteristic velocity of the system and c. This characteristic velocity is proportional to the nuclear charge Z (note that the kinetic energy is proportional to Z ). The parameter that monitors relativistic effect is therefore Zc, even if formally c appears as perturbation parameter. 

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