The vertical diffusivity and mean velocity of particles in a horizontal water pipe

Abstract

Small spheres of the same size but of relative density varying from 0·92 to 1·25 were injected in turn into a horizontal water pipe, in which the flow was turbulent and the mean velocity was constant. A cross-section near the outlet was illuminated; the positions of the spheres as they crossed it were measured by photography, and the relation was established between the terminal velocity of the of the spheres in water and the vertical diffusivity. The velocity of the spheres along the pipe was found to be somewhat different in the galvanized steel and Perspex lengths of which the pipe was composed. The dispersion of the times of transit of the spheres increased slightly with their densisty. For purposes of comparison the theoretical velocity along the pipe was also calculated from the photographic measurements.

Longitudinal instability of slurry pipeline flow

“…6 and 11 (for more details on this point, see e.g. Barnard and Binnie (1963) , Karabelas (1977) , Kaushal and Tomita (2002) and Kaushal and Tomita (2013) ). A further approximation is the assumption that the axial velocity u x ( r ) obeys a "similarity-law"-type dependence on the radial pipe coordinate:…”

“…From this relation, we estimate that at a distance of 0.25 m from the pipe wall, in a flow with an average velocity of 1.5 m/s, ū /u * ≈ 30 , hence q ≈ 36.7. Now we tackle the calculation of : Barnard and Binnie (1963) , Karabelas (1977) , Kaushal and Tomita (2002) and Kaushal and Tomita (2013) , it appears that the value ζ = 0 . 25 is an adequate approximation.…”

“…Consequently, relatively small variations in ζ can have a large impact on this conversion factor. From the existing papers on turbulent diffusivity of slurries in pipelines (see Barnard and Binnie (1963) , Karabelas (1977) , Kaushal and Tomita (2002) and Kaushal and Tomita (2013) ), it is clear that the value of ζ used in the current study is by no means "cast in stone". This implies a certain degree of uncertainty in our statements regarding the time that is needed for plugs to develop to full maturity.…”

Transport characteristics of suspensions: Part IX. Representation of periodic phenomena on a flow regime diagram for dilute suspension transport

“…A generalized flow regime diagram for suspension transport may be prepared by combining the results of (6) and Newton's law (500 < D p U t / v ) (7) For a given system these 45-deg. lines represent constant particle size; consequently as the fluid velocity is increased, the data fall along these lines from the upper left to the lower right.…”

“…The first step is to determine the particle Reynolds number D p U t / v . The terminal-settling velocity can be calculated from either Equations ( 5 ) , (6), or ( 7 ) , or it can be determined from available charts (26); the result is Ut = 0.172 ft./sec., corresponding to a Reynolds number of 20. When one follows the line for N R~ = 20 from left to right on Figure 3, the values of D p u0*/v corresponding to the beginning of the different regimes can be read from the intersection with the appropriate lines.…”