Centrifugal force term

Figure 9 The normalized vibrational friction felt by a range of diatomic solutes dissolved in liquid carbon dioxide and liquid acetonitrile (62). The solutes are meant to represent the nondipolar molecule Br2 itself and two bromine mimics differing only in the replacement of the bromine quadrupole by permanent dipoles of different strengths. The d5 solute has a dipole moment of 5.476 D and the d8 solute a dipole moment of 8.762 D. (The notation r/vv emphasizes the fact that only potential-energy contributions are included in the calculations centrifugal force terms are neglected.)...

Note that the centrifugal force term, in the angular momentum quantum number /, is zero for s orbitals. While each of these simple integrals has an analytical solution, we can now apply the numerical procedures of Chapter 2 directly to equation 4.14 and determine the energy of this Is trial function. Since this is the exact Is orbital for the hydrogen atom, this exercise functions also as a good test of the integration procedure. 

In a rotating flow, the BBOT equations therefore describe a centrifugation movement of a small particle, the characteristics of which ate driven by rather simple mechanisms. The duration of the transient regime before equilibrium between the centrifugal forcing term and the friction is very short. The centrifugation process is described approximately by ... 

We are neglecting the gas density in comparison to the solid density in the centrifugal force term (Chap. 2). Equating these forces to find the cut size 0 50 gives ... 

Other Centrifugal Collectors. Cyclones and modified centrifugal collectors are often used to remove entrained Hquids from a gas stream. Cyclones for this purpose have been described (167—169). The rotary stream dust separator (170,171), a newer dry centrifugal collector with improved collection efficiency on particles down to 1—2 pm, is considered more expensive and hence has been found less attractive than cyclones unless improved collection in the 2—10-pm particle range is a necessity. A number of inertial centrifugal force devices as well as some others termed dynamic collectors have been described in the Hterature (170). 

The centrifugal force produced increases the impeller static pressure [the first term of the right-hand side of Eq. (9.79)] and reduces the relative velocity U2 To increase the static pressure by a change in the relative velocity, the following relationship is necessary ... 

When rotation occurs, static imbalance translates into a centrifugal force. As a result, this type of imbalance is sometimes referred to as force imbalance and some balancing machine manufacturers use the word force instead of static on their machines. However, when the term force imbalance was just starting to be accepted as the proper term, an American standardization committee on balancing terminology standardized the term static instead of force. The rationale was that the role of the standardization committee was not to determine and/or correct right or wrong practices, but to standardize those currently in use by industry. As a result, the term static imbalance is now widely accepted as the international standard and, therefore, is the term used in this chapter. 

This inward force has a real agent, namely, a tension of the cord, which is applied to the body. The same cord acts on the pin with a force, which has the same magnitude as that of the centripetal one but opposite direction. This force has the same physical origin, (deformation of cord) and it is called the centrifugal force. The term centrifugal means literally fleeing a center . Centripetal and centrifugal forces always form a pair of action and reaction and they are applied to different parts of the system. In our case these parts are a small body and a pin. 

Here p is the pressure, ga the field of attraction, 5 the density of the fluid, and r the vector directed away from the axis of rotation and it is equal in magnitude to the distance between a particle and this axis. The first two terms of Equation (2.332) characterize the real forces acting on the particle, namely the surface and attraction ones. At the same time the last term is a centrifugal force, and it is introduced because we consider a non-inertial frame of reference. It is convenient to represent Equation (2.332) as... 

It is instructive to express e in terms of the ratio of the centrifugal force and the gravitational field at points at the equator... 

Until this point, the sample preparation techniques under discussion have relied upon differences in polarity to separate the analyte and the sample matrix in contrast, ultraflltration and on-line dialysis rely upon differences in molecular size between the analyte and matrix components to effect a separation. In ultrafiltration, a centrifugal force is applied across a membrane filter which has a molecular weight cut-off intended to isolate the analyte from larger matrix components. Furusawa incorporated an ultrafiltration step into his separation of sulfadimethoxine from chicken tissue extracts. Some cleanup of the sample extract may be necessary prior to ultrafiltration, or the ultrafiltration membranes can become clogged and ineffective. Also, one must ensure that the choice of membrane filter for ultrafiltration is appropriate in terms of both the molecular weight cut-off and compatibility with the extraction solvent used. 

B. The second term in Eq. (F) generally becomes important at large values of J when centrifugal force increases the separation between atoms. 

The force on a sedimenting particle increases with the velocity of the rotation and the distance of the particle from the axis of rotation. A more common measurement of F, in terms of the earth s gravitation force, g, is relative centrifugal force, RCF, defined by Equation 7.2. 

Although this introduction outlines the basic principles of centrifugation, it does not take into account other factors that influence the rate of particle sedimentation. Centrifuged particles migrate at a rate that depends on the mass, shape, and density of the particle and the density of the medium. The centrifugal force felt by the particle is defined by Equation 7.1. The term m is the effective mass of the particle, that is, the actual mass,... 

It is cumbersome and sometimes impractical to express sedimentation velocity in terms of p, v, and/ since these factors are difficult to measure. A new term, sedimentation coefficient, s (the ratio of sedimentation velocity to centrifugal force) is introduced by rearranging Equation 7.7 to Equation 7.8. 

This is called the radial wave equation. Apart from the term involving l, it is the same as the one-dimensional time-independent Schrodinger equation, a fact that will be useful in its solution. The last term is referred to as the centrifugal potential, that is, a potential whose first derivative with respect to r gives the centrifugal force. 

Under the centrifugal force, the acceleration term in Eq. (10.5) becomes... 

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