Radial Distance

Centrifugal separators make use of the common principle that an object whirled about an axis at a constant radial distance from the point is acted on by a force. Use of centrifugal forces increases the force acting on the particles. Particles that do not settle readily in gravity settlers often can be separated from fluids by centrifugal force. 

The pressure drop around the wellbore of a vertical producing well is described in the simplest case by the following profile of fluid pressure against radial distance from the well. 

Eddy currents and the magnetic flux that is associated to them are proportional to the radial distance of the coil center. The magnetic flux is proportional to the probe induction and consequently to the passing current. The theoretic calculation of this induction is given by the following equation ... 

Spherically symmetric (radial) wave functions depend only on the radial distance r between the nucleus and the election. They are the Is, 2s, 3s. .. orbitals... 

For the atomic orbital = e where r is the radial distance between the proton and the electron, show that [Eq. (6-21)]... 

There exists some radial distance from the axis of rotation at which all of the mass could be concentrated to produce the same moment of inertia that the actual distribution of mass possesses. This distance is defined to be the radius of gyration. According to this definition,... 

Fig. 19. Comparison of the predictions of k-e model and experimental data for a confined swirling flow, (a) Flow configuration where 4. is the primary inlet, D = 25 mm, and B is the secondary inlet, = 31 mm, = 59 mm and the step height, H = 31.5 mm. (b) Predicted and measured streamline values where r/H is the ratio of the radial distance from the centerline to the step height.

Pattemators may comprise an array of tubes or concentric circular vessels to coUect Hquid droplets at specified axial and radial distances. Depending on the pattemator, various uniformity indexes can be defined using the accumulated relative values between the normalized flow rate over a certain sector or circular region and a reference value that represents a perfectly uniform distribution. For example, using an eight-sector pie-shaped coUector, the reference value for a perfectly uniform spray would be 12.5%. The uniformity index (28) could then be expressed as foUows, where is the normalized volume or mass flow rate percentage in each 45-degree sector. 

Whatever the mechanism and the method of operation, it is clear that the leaching process will be favored by increased surface per unit volume of sohds to be leached and by decreased radial distances that must be traversed within the solids, both of which are favored by decreased particle size. Fine solids, on the other hand, cause slow percolation rate, difficult solids separation, and possible poor quahty of sohd product. The basis for an optimum particle size is estabhshed by these characteristics. 

According to these equations, ion concentration is directly proportional to the crjrona voltage and inversely proportional to the radial distance. Equation... 

FIGURE 13.10 Electric field as a function of radial distance (tubular geometry). 

So, for some match point / to infinity, the atomic pseudo-orbital is identical to the valence HF atomic orbital. For radial distances less than / the pseudoorbital is defined by a polynomial expansion that goes to zero. The values of the polynomial are found by matching the value and first three derivatives of the HF orbital at / . 

The shortest stack exists when q j = 3,300 BTU/hr sq ft (Figure 7-76). The limiting radial distance from the flame, allowing for speed of escape of 20 ft/sec is [60] ... 

D = X = radial distance from flame core (center) to grade, ft... 

R = y = radial distance from base of stack, ft, to grade intersection with D q = time interval for escape, sec... 

The nip is the radial distance or V formed between rolls on a line of centers. In-going safety devices in the nip areas are built into these machines. They protect the hands of operators. An emergency stop device is placed in an accessible location on the upstream side. 

It is further assumed that the mesophase layer consists of a material having progressively variable mechanical properties. In order to match the respective properties of the two main phases bounding the mesophase, a variable elastic modulus for the mesophase may be defined, which, for reasons of symmetry, depends only on the radial distance from the fiber-mesophase surface. In other words, it is assumed that the mesophase layer consists of a series of elementary peels, whose constant mechanical properties differ to each other by a quantity (small enough) defined by the law of variation of Ej(r). 

---