Radial, force

There are two main reasons why a pump should not operate below its MCSF (/) the radial force (radial thmst) is increased as a pump operates at reduced flow (44,45). Depending on the specific speed of a pump, this radial force can be as much as 10 times greater near the shut off, as compared to that near the BEP and (2) the low flow operation results in increased turbulence and internal flow separation from impeller blades. As a result, highly unstable axial and radical fluctuating forces take place. 

As compression occurs concurrently in both halves of the compressor, radial forces are oppositely directed, resulting in negligible net-radial loads on the rotor bearings (uuhke twin screw compressors), but there are some loads on the star wheel shafts. 

The normal operating position of a shaft inside a bearing is shovvm in Fig, 29-64, It can be seen that, due to radial forces, the geometric center of the shaft does not coincide with the one of the bearing. This displacement creates a vv edge, vvFich combined with the shaft motion, forces the oil into a continiioiislv decreasing area, and a... 

The radial forces acting on the bearing can be determined by the belt pull and is expressed by... 

Transmission of load and suitability of bearings 8/217 Radial forces on bearings... 

RADIAL FORCE VS. DESIGN CAPACITY WITH A SINGLE AND DOUBLE VOLUTE... 

Iversen, H. W., Rolling, R. E., Carlson, J. J. Volute pressure distribution, radial force on the impeller and volute mixing losses of a radial flow centrifugal pump. Trans. ASME, journal of Engineering for Tower 82 (1.960), pp. 136-144. 

A radial force on the pipe wall ahead of the deflagration wave. There is a varying pressnre between the aconstic wave and the flame front where the pressnre bnilds from near atmospheric pressnre, Pi (step change at the wave front) to eight times Pi (or higher) at the flame front. The pressnre ratios depend on the flame acceleration. There is no snch effect with a detonation. 

A radial force on the pipe watt behind the flame front. For a closed pipe, this remains constant (at abont STi) everywhere for a deflagration, bnt decays from abont 20Ti to STi behind the detonation over most of the pipe length. 

For example, mechanical imbalance generates radial forces in all directions, but misalignment generally results in a radial force in a single direction that corresponds with the misaligned direction. The ability to determine the actual displacement direction of the machine s shaft and other components greatly improves diagnostic accuracy. 

Self-expanding stents with a higher radial force (e.g., WingSpan, Boston Scientific Corp.) will probably play a key role in acute stroke cases related to intracranial atherosclerotic disease. Antegrade flow is essential for the maintenance of vascular patency, as particularly evident in patients with severe proximal stenoses who commonly develop rethrombosis after vessel recanalization. Furthermore, stenting of the proximal vessels may be required in order to gain access to the intracranial thrombus with other mechanical devices or catheters. In a recent series, 23 of 25 patients (92%) with acute n = 15) or subacute n = 10) ICA occlusions were successfully revascularized with this technique. " ... 

Figure 14. Distribution of turgor-induced stresses at a tricellular junction. FT is the con nent of the stress in the plane of each cell wall and FC is the radial force separating the cells at the comers.

This also applies to a body submerged in a fluid that is subject to any acceleration. For example, a solid particle of volume Vs submerged in a fluid within a centrifuge at a point r where the angular velocity is on is subjected to a net radial force equal to Ap on2rVs. Thus, the effect of buoyancy is to effectively reduce the density of the body by an amount equal to the density of the surrounding fluid. 

A simplified schematic of a particle in a centrifuge is illustrated in Fig. 12-3. It is assumed that any particle that impacts on the wall of the centrifuge (at r2) before reaching the outlet will be trapped, and all others won t. (It might seem that any particle that impacts the outlet weir barrier would be trapped. However, the fluid circulates around this outlet corner, setting up eddies that could sweep these particles out of the centrifuge.) It is thus necessary to determine how far the particle will travel in the radial direction while in the centrifuge. To do this, we start with a radial force (momentum) balance on the particle ... 

Substitution of Equation (3.62) into Equation (3.60) gives the relative zero shear viscosity. When the shear rate makes a significant contribution to the interparticle interactions, the mean minimum separation can be estimated from balancing the radial hydrodynamic force, Fhr, with the electrostatic repulsive force, Fe. The maximum radial forces occur along the principle axes of shear, i.e. at an orientation of the line joining the particle centres to the streamlines of 6 = 45°. This is the orientation shown in Figure 3.19. The hydrodynamic force is calculated from the Stokes drag, 6nr 0au, where u is the particle velocity, which is simply... 

The radius at which a particle will rotate within the body of a cyclone corresponds to the position where the net radial force on the particle is zero. The two forces acting are the centrifugal force outwards and the frictional drag of the gas acting inwards. 

If the radial velocity is low, the inward radial force due to friction will, from Chapter 3, be equal to 3jtp,dur, where /x is the viscosity of the gas, and ur is the radial component of the velocity of the gas. 

In a spin-filter based stirred bioreactor, there are various forces acting on both the liquid medium and the cell particles gravity force, axial force due to impeller rotation, centrifugal force created by the spin-filter rotation, and radial force (drag) generated by the perfusion flux. 

Fig. 2.15 Top view (z face) of the differential element used to illustrate the contribution to the radial force balance.

It is evident that the contributions due to angular movements are caused by diffusion forces corresponding to the state of orientation, whereas the radial component is a hydrodynamic contribution. The radial force, as exerted by the flowing solvent, is balanced by the rigidity of the rod and has no consequences for the birefringence of orientation. According to eqs. (5.15), one obtains for rigid dumb-bells ... 

Millman, B. M., and Irving, T. C. (1988). Filament lattice of frog striated muscle. Radial forces, lattice stability, and filament compression in the A-band of relaxed and rigor muscle. Biophys.J. 54, 437-47. 

Thus, the r and components of the velocity gradient are completely disregarded and Vq1 depends on those coordinates only through the r and dependence of the (radial) force density and the ground state shear velocity. The quality of this model increases with increasing kR. It is expected that the velocity perturbation is overestimated in this model and thus the hypothetical instability threshold is lowered, which makes the model appealing at least as a first attempt. 

Normal stress differences also have practical relevance for extrusion They assist in centering the shaft in the extruder when processing thermoplastics as the rotation of the screw generates radial forces (from the shaft to the wall). 

By performing a radial force balance, Spieiman and Fitzpatrick (1973) determined the radial velocity of a particle attracted to a spherical collector by Loudon forces when particle inertia and Brownian motion are... 

Covalent Solids. Interatomic potentials are the most difficult to derive for covalent solids. The potential must predict the directional nature to the bonding (i.e. the bond angles). Most covalent solids have rather open crystal stmctures, not close packed ones. Pair potentials used with diatomic molecules, such as the Lennard-Jones and Morse potentials, are simply not adequate for solids because atoms interacting via only radial forces prefer to have as many neighbors as possible. Hence, qualitatively wrong covalent crystal stmctures are predicted. 

Chadi and Martin (1976) used essentially the same LCAO parameters that are given in the Solid State Table to obtain the energies at the two special points in the Brillouin Zone. They then redetermined the wave numbers of the special points for the distorted crystal and recalculated the energy. The clastic distortion which they used is a shear strain, in which there is no change in bond length to first order in the strain thus the radial force constant ofEq. (8-1) docs not enter the calculation. That strain can be written as... 

The fourth complication is the tendency toward internal displacements, displacements of the two atoms in the primitive cell with respect to each other. We see in particular that radial interactions tend to pull the central atom upward (in the x-dircclion) under this distortion. Similarly, the tendency to maintain tetrahedral angles will push the central atom in the opposite direction. Radial forces always win. These displacements are the origin of piezoelectricity and we shall return to them in Section 8-E. 

In the zincblende structure, with three independent elastic constants, the use of a model with only two parameters will allow a test and also allows alternate ways of obtaining the parameters. We obtain the radial force constant from a uniform compression, e, = = Cj = r, from which we obtain a change in energy per bond... 

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