The centrifugal force

As a rule, geophysical literature describes the rotation of a particle on the earth surface with the help of the attraction force and the centrifugal force. It turns out that the latter appears because we use a system of coordinates that rotates together with Earth. As we know Newton s second law, wa = F, is valid only in an inertial frame of reference, that is, the product of mass and acceleration is equal to the real force acting on the particle. However, it is not true when we study a motion in a system of coordinates that has some acceleration with respect to the inertial frame. For instance, it may happen that there is a force but the particle does not move. On the contrary, there are cases when the resultant force is zero but a particle moves. Correspondingly, replacement of the acceleration in the inertial frame by that in a non-inertial one gives a new relation between the acceleration, mass, particle, and an applied force  

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. 

Now we focus on pseudo forces and, first, consider a two-dimensional case. 

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The simplest type of centrifugal device is the cyclone separator (Fig. 3.4), which consists of a vertical cylinder with a conical bottom. The centrifugal force is generated by the fluid motion. The mixture enters in a tangential inlet near the top, and the rotating motion so created develops centrifugal force which throws the particles radially toward the wall. 

Figure 3.5 shows centrifuges in which a cylindrical bowl is rotated to produce the centrifugal force. In Fig. 3.5a, the cylindrical bowl is shown rotating with a feed consisting of a solid-liquid mixture admitted at the center. The feed is immediately thrown outward toward the walls of the container. The particles settle horizontally... 

Cyclones. Cyclones are also primarily used as prefilters. These also were discussed in Chap. 3 and illustrated in Fig. 3.4. The particle-laden gas enters tangentially and spins downward and inward, ultimately leaving the top of the unit. Particles are thrown radially outward to the wall by the centrifugal force and leave at the bottom. 

The general analysis, while not difficult, is complicated however, the limiting case of the very elongated, essentially cylindrical drop is not hard to treat. Consider a section of the elongated cylinder of volume V (Fig. II-18h). The centrifugal force on a volume element is u rAp, where w is the speed of revolution and Ap the difference in density. The potential energy at distance r from the axis of revolution is then w r Apfl, and the total potential energy for the... 

Secondly, the centrifugal force on the ion as its path is deflected by a magnetic field is equal to the force exerted by the field on a moving charge (Equation 24.2). 

The scale-up of filtration centrifuges is usually done on an area basis, based on small-scale tests. Buchner funnel-type tests are not of much value here because the driving force for filtration is not only due to the static head but also due to the centrifugal forces on the Hquid in the cake. A test procedure has been described with a specially designed filter beaker to measure the intrinsic permeabiHty of the cake (7). The best test is, of course, with a small-scale model, using the actual suspension. Many manufacturers offer small laboratory models for such tests. The scale-up is most reHable if the basket diameter does not increase by a factor of more than 2.5 from the small scale. 

The criterion bv which the baU action in mills of various sizes may be compared is the concept of critical speed. It is the theoretical speed at which the centrifugal force on a ball in contacl with the mill shell at the height of its path equals the force on it due to gravity ... 

Another advantage of the radial reacrion turbine is that it can be designed to accept condensation in any amount without efficiency deterioration or erosion. This is possible because there are two forces acring on suspended fog particles, the deceleration force and the centrifugal force, and these two forces can be balanced against each other to prevent the droplets from impinging on specially shaped blades. The process is expl ned as follows ... 

In the friction layer where the isobars are curved, the effect of frictional drag is added to the forces discussed under gradient wind. The balance of the pressure gradient force, the coriolis deviating force, the centrifugal force, and the frictional drag in the vicinity of the curved isobars results in wind flow around low pressure and high pressure in the Northern Hemisphere, as shown in Fig. 17-16. 

For any cyclone, regardless of type, the radius of motion (curvature), the particle mass, and the particle velocity are the three factors which determine the centrifugal force exerted on the particle. This centrifugal force may be expressed as... 

Most seal manufacturers limit the speed of their seals to 90fps (27.4 mps) with good lubrication of the faces. This is primarily due to the centrifugal forces acting on the seal which tend to restrict its axial flexibility. 

This force must be balanced by the centrifugal force of the ion mv /r, where r is the radius of curvature of the trajectory. Hence,... 

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