Flow region

Here (0 is the magnitude of the vorticity vector, which is directed along the z axis. An irrotational flow is one with zero vorticity. Irro-tational flows have been widely studied because of their useful mathematical properties and applicability to flow regions where viscous effects m be neglected. Such flows without viscous effec ts are called in viscid flows. 

The discharge coefficient for the screen C with aperture D, is given as a function of screen R nolds number Re = D,(V/d) /[L in Fig. 6-16 for plain square-mesfi screens, Ot = 0.14 to 0.79. This cui ve fits most of the data within 20 percent. In the laminar flow region, Re < 20, the discharge coefficient can be computed from... 

A turbulent free jet is normally considered to consist of four flow regions (Tuve, Heat. Piping Air Cond., 25(1), 181-191 [1953] Davies, Turbulence Phenomena, Academic, New York, 1972) as shown in Fig. 6-17 ... 

Several references quote a length of 100 nozzle diameters for the length of the estabhshed flow region. However, this length is dependent on initial velocity and Reynolds number. 

David W. Taylor Model Basin, Washington, September 1953 Jackson, loc. cit. Valentin, op. cit.. Chap. 2 Soo, op. cit.. Chap. 3 Calderbank, loc. cit., p. CE220 and Levich, op. cit.. Chap. 8). A comprehensive and apparently accurate predictive method has been publisned [Jami-alahamadi et al., Trans ICE, 72, part A, 119-122 (1994)]. Small bubbles (below 0.2 mm in diameter) are essentially rigid spheres and rise at terminal velocities that place them clearly in the laminar-flow region hence their rising velocity may be calculated from Stokes law. As bubble size increases to about 2 mm, the spherical shape is retained, and the Reynolds number is still sufficiently small (<10) that Stokes law should be nearly obeyed. 

Visual examination of external surfaces revealed grooves and general metal loss (Figs. 7.24 and 7.25). Metal loss was caused by erosion-corrosion. However, the corrosive loss was more important than erosive loss, since metal loss was also substantial in low-flow regions. 

Figure 8-41. Unstable flow region of a centrifugal compressor curve.

Figure 7-20. A-faotor versus Reynolds number in the laminar flow region 10 < Npg < 2,000. (Source Chen, S. J., Kenics technical data KTEK-2, 1978.)...

The flow region between laminar and turbulent flow is called transitional flow. It is three dimensional and varies with time. 

The flow is turbulent, Re > 2300, and thus the part of Eq. (4.201) that considers the inlet flow region = 1 can be ignored. 

Velocity measurements in flow regions where other devices fail to operate suitably—boundary layers, stagnating air zones—are typical applications. 

High-energy ignition of an unobstructed cloud by a jet flame emerging from a partially confined explosion produces a high combustion rate in the jet-flow region. 

VTien the Reynolds number is below a value of 2000, the flow region is considered laminar. The pipe friction factor is defined as ... 

However, on die basis of the relation between pressure drop and die minimum fluidisation velocity of particles, the point of transition between a packed bed and a fluidised bed has been correlated by Ergun41 using (17.7.2.3). This is obtained by summing the pressure drop terms for laminar and turbulent flow regions. 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

As indicated earlier, non-Newtonian characteristics have a much stronger influence on flow in the streamline flow region where viscous effects dominate than in turbulent flow where inertial forces are of prime importance. Furthermore, there is substantial evidence to the effect that for shear-thinning fluids, the standard friction chart tends to over-predict pressure drop if the Metzner and Reed Reynolds number Re R is used. Furthermore, laminar flow can persist for slightly higher Reynolds numbers than for Newtonian fluids. Overall, therefore, there is a factor of safety involved in treating the fluid as Newtonian when flow is expected to be turbulent. 

Between the laminar and turbulent zones, there exists a transition region in which the viscous arid inertial forces are of comparable magnitudes. No simple mathematical relationship exists between Np and Re in this flow region and, at a given value of Re, N p must be obtained from the appropriate power curve. 

In fact a parabolic surface of the rolls in the flow region is assumed, which is valid as long as the rolling bank diameter is small compared with the roll diameter. This is normally the case in a calendering process. 

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