incorrect and functional, because of the relative insensitiveness of the mean properties, such as c, on the space dependence of DL. [An analogous coincidence permits the acceptable usage of phenomenological theories (such as Prandtl's mixing length, Taylor's vorticity transfer, and Von K h r m h ' s similarity), all physically inaccurate, for the prediction of mean flow properties (Hinze, 1959).] A very acceptable expression for the dispersion coefficient was presented by Taylor (1954). The authors call this a virtual coefficient of diFfusion and seemingly fail to recognize its equality to DL. Taylor combined both the radial and convective dispersion coefhients, given by Kradial= 0.05 au* and Kconveotlve = 10.06 au, to give what is interpreted as the longitudinal dispersion coefficient
DL
10.1 au*
=
(3)
where (following Taylor's notation) a is the pipe radius and u* is the wall friction velocity (also called shear velocity, but incorrectly identified by the authors as the turbulent velocity). The relationship suggested by the authors to predict the dispersion coefficient is an empirical best fit Equation 34.
DL = 3.87
>:
sq. ft./sec.
(4)
Even though an acceptable fit of their data, the relationship is not sufficiently general. First, it relates a dimensionless grouping, the Reynolds number, with a dimensional coefficient, DL. Second, ihe power on the Reynolds number in Equation 3 lacks physical significance and is strongly dependent on the experimental data. The authors' flow field consisted of a fully developed t u bulent pipe flow. For such, Equation 35 (the Blasius empirical results) and ~~~~~i~~ 2,6(a Statement of linear momentum conservation), may be combined to give : u-., ~- 0.1989 -
The above is valid for all fully developed turbulent pipe flows. The authors do not report the temperature of the water in the test section, but considering the described experimental setup, a temperature of 65' F. would seem logical to assume; hence if Y is in square feet per second, au, =
1.127 X
Re7l8
Combining with Equation 4,
DL = 34.34 Re-O.111
-
au
*
The authors' experimental results were limited to lo4 < Re < 2 X lo5. (They clearly state that their model was valid for R e greater than lo4, but failed to explain that there will also be an upper bound.) For the range of their tests then, 8.8
DL
