Axial distance

Practical applications [2] of a GammaMat M model using the new Selenium crawler camera loaded with approx. 1 TBq (30Ci) on a pipeline of diameter 12 and wall thickness of 0.25 showed 6-7 m axial distance to the exposed source as limit of the radiation controlled area (40pSv/h) and 22m perpendicular to the pipeline. Other authors [3] have reported about a comparison for Ir-192 and Selenium source on a 4.5 diameter pipe and 0,125 steel thickness they have found for 0.7 Tbq (18Ci) Selenium a value of 1 Om behind the film (in the unshielded beam) comparing under same conditions to approx. 40m for Iridium. 

Figure 5 shows the variation of the droplet mean axial velocity at the same axial location. The primary feature of this velocity profile is that the maximum velocity peaks at the centerline. The velocity magnitude and direction in the center region tend to be related to the hquid swid strength and axial distance. A reverse (recirculation) flow with negative velocity is possible if the swid is intense. Under such conditions, the maximum velocity tends to shift away from the centerline. 

Transmission of Forces As pressure is applied to a powder in a die or roll press, various zones in the compact are subjected to differing intensities of pressure and shear. Compaction stress decreases with axial distance from the applied pressure [Strijbos et al.. Powder Tech., IS, 187 209 (1977)] due to frictional properties of the powder and die wall. For example, the axialpressure experienced within a cyhndrical die with an applied axial loaa Oq may be estimated to a first approximation by... 

The jet will separate from the surface if the axial distance between the slot and the obstruction, x, is less than a specified critical distance x,. (Fig. 7,41). The... 

The rotor is designed much like a screw thread. The rotor pitch is equivalent to the wavelength of the rotor. The rotor lead is the axial distance that a wave advances during one full revolution of the rotor. The rotor pitch and the stator pitch are equal. The rotor lead and stator lead are proportional to their respective number of waves. Thus, the relationship between rotor pitch (in.) and stator pitch, t (in.) is [86]... 

Fig. 45. Radial strain rate distribution function and its influence on the degradation yield O (r0 orifice radius, r axial distance from the orifice center) C(r2/r0) variation of the strain rate as a function of (r/r0)2 obtained from the reciprocal of the degradation yield curve of a monodisperse polymer fraction (see Fig. 46) C(r/r0) radial distribution of the strain rate in the plane of the orifice, calculated from the function C(r2/rg)...

The dependence of the local Nusselt number on non-dimensional axial distance is shown in Fig. 4.3a. The dependence of the average Nusselt number on the Reynolds number is presented in Fig. 4.3b. The Nusselt number increased drastically with increasing Re at very low Reynolds numbers, 10 < Re < 100, but this increase became smaller for 100 < Re < 450. Such a behavior was attributed to the effect of axial heat conduction along the tube wall. Figure 4.3c shows the dependence of the relation N /N on the Peclet number Pe, where N- is the power conducted axially in the tube wall, and N is total electrical power supplied to the tube. Comparison between the results presented in Fig. 4.3b and those presented in Fig. 4.3c allows one to conclude that the effect of thermal conduction in the solid wall leads to a decrease in the Nusselt number. This effect decreases with an increase in the... 

Fig. 4.3a-c Experimental results for smooth circular tubes, (a) Dependence of the Nusselt number on non-dimensional axial distance rfin = 125.4, 300 and 500 pm, Re = 95—774. Reprinted from Lelea et al. (2004) with permission, (b) d =... 

Warrier et al. (2002) conducted experiments of forced convection in small rectangular channels using FC-84 as the test fluid. The test section consisted of five parallel channels with hydraulic diameter = 0.75 mm and length-to-diameter ratio Lh/r/h = 433.5 (Fig. 4.5d and Table 4.4). The experiments were performed with uniform heat fluxes applied to the top and bottom surfaces. The wall heat flux was calculated using the total surface area of the flow channels. Variation of single-phase Nusselt number with dimensionless axial distance is shown in Fig. 4.6b. The numerical results presented by Kays and Crawford (1993) are also shown in Fig. 4.6b. The measured values agree quite well with the numerical results. 

T = reactor residence time Z = dimensionless axial distance... 

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

At large distances from the nozzle, the axial velocity exhibits self-preserving similarity in that, when plotted in the above dimensionless form, velocity profiles at all cross-sections downstream collapse onto a single curve. It is probable that strict similarity is preserved only at axial distances in excess of 30-40 diameters. However, the above formulation is frequently used to describe the velocity profile at all points downstream of the flow development region. For work performed with M. citrifolia, the numerical values recommended by Panchapakesan and Lumley [131] for the constants K and C in Eqs. (12) and (13), i.e. 75.2 and 6.06, respectively, are employed. 

In terms of shear stress levels in the developed flow field, the maximum stress [131] occurs at an axial distance between 6 and 7 nozzle diameters downstream and is given by ... 

In the above equations, flie dimensionless substrate concentration, Yj, ami the dimensionless axial distance Z... 

In the above case, D is an eddy dispersion coefficient and Z is the axial distance along the reactor length. When combined with an axial convective flow contribution, and considering D as constant, the equation takes the form... 

This example models the dynamic behaviour of an non-ideal isothermal tubular reactor in order to predict the variation of concentration, with respect to both axial distance along the reactor and flow time. Non-ideal flow in the reactor is represented by the axial dispersion flow model. The analysis is based on a simple, isothermal first-order reaction. 

T Distance zfco/v)1 2 Z = axial distance v = kinematic viscosity to = radial velocity... 

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