## A GENERAL THEORY OF THE HYDRAULIC

TRANSPORT OF SOLIDS IN
FULL SUSPENSION

By A C Bonapace

**VII. COMPARISON OF EXPERIMENTAl RESULTS WITH**

THOSE OBTAINED FROM THE THEORY

Sixteen cases of hydraulic transport are to be discussed and presented in their main operative parameters as per Table 1. Column 1 of
Table 1 carries an internal reference number. Column 2 carries the
literature reference number of the publication from which information was
extracted and in brackets the reference figures. Column 3 carries the solid-water density ratio = 1 + μ, Column 4 the pipe diameter D, Column 5 the particle diameter d, Column 6 the relative roughness of the
pipe Column 7 the friction factor f_{μo}, Column 8 the suspension velocity V_{μo} and Column 9 the hydraulic gradient I_{μo} associated with V_{μo} (cf Eq.
3.2). In Table 1 the solid concentration does not appear as one refers to
one small particle only, present.

In Table 2 quantities are expressed in a non-dimensional form as per Eqs. (2.16) and (2.17).

Columns 1, 2 and 6 of Table 2 are just a repetition of the corresponding columns 1, 3 and 7 of Table 1. Column 3 and 5 carry nondimensional values of the pipe diameter D_{μo} and of the velocity V_{μo} of
Table 1. Calculation of α by Eq. (5.4) has enabled the definition of Ω_{10} and in the generating plane. In Table 3 the tabulated quantities refer to a field with μ ≠ 0 and x > 0. With Column 1 used as reference, the quantities 1 + μ, , and in Columns 2, 3, 4 and 5 are those of the corresponding Columns 2, 3 4 and 5 of Table 2. Column 6 carries the
hydraulic gradient (already reported in Table 2 by Column 7). Column 7, 8 and 9 carry the concentration x, x^{1/2} and βx^{1/2} in its various forms.
Columns 10 and 11 carry the stream velocity Ω_{μβx} and the hydraulic
gradient referred to conditions μ βx respectively. Column 12 carries
the experimental hydraulic gradient measured graphically in the plane of representation of the test results. Column 13 carries the ratio between the calculated values of Iμβx and the experimental ones

Many values of Ω_{μβx} and calculated according to the theory could not be analysed by comparison. Their experimental counterparts could not be ascertained, being the experimental field too narrow.

With reference to experiment 8 the original percental concentration by weight has been reduced by the author to a volumetric concentration.

Hence Table 3 covers twenty-four results verified experimentally and two results obtained by extrapolation.

As a graphical illustration of the method let one refers to experiment
5 and to the corresponding Fig. 4 (retraced by the author). The experiment
deals with the hydraulic transport of gravel

Characteristical loci are shown in a representation hydraulic gradient versus a nominal velocity V (solid + liquid):

A locus for water only and five loci of increasing volumetric concentrations x = 0,05; 0,10; 0,15; 0,20 and 0,25 have been drawn:

In Table 3 at reference 5 one has reported values of Ω_{μo} and and then values Ω_{μβx} and with representative points falling close to the
corresponding characteristical loci for x = 0,05; 0,10 and 015.

For the value x = 0,20 the representative point has been extrapolated as shown. Hence in Fig. 4 a locus DC (in dotted line) has been drawn
joining all the points obtained by the theory.

The statistical analysis of the twenty-four numerical results of Column
14 (results by extrapolation excluded) yields a mean close to 1
(0,982) and a standard deviation σ = 0,050.

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