## A GENERAL THEORY OF THE HYDRAULIC

TRANSPORT OF SOLIDS IN
FULL SUSPENSION

By A C Bonapace

**I. INTRODUCTION**

In the present paper particle transport by a stream is considered with particles conveyed in a fully suspended state. In a well-known work,
Durand and Condolios [2] correlated many experimental results of transport
in water, with particles having some intermittent contact with the
boundary. The authors however did not define sufficiently the condition
by which the considered slurries would proceed with the solid phase fully
suspended inside the fluid. It is the object of the present paper to define
this "suspension" phenomenon both for a single particle present in the
system as well as for many particles transported, i.e. for a certain finite
volumetric concentration of the solid material.

The results obtained from the present analysis of sixteen experimental
cases of hydraulic transport of particles settling in water have been
found to agree with the results of the analysis herein established.

The results could be further extended to particles buoyant in a fluid
and to particles transported in gas streams, (e.g. air) i.e. with relative
density of the solid phase a few thousand times greater than the fluid.

Hence this presents possibility to forecast the conditions of transport
in full suspension for different solids in a great variety of vector fluids.

Operating with non-dimensional quantities further widened the generality
of the results. By this the obtained literary expressions resulted
independent of the kinematic viscosity of the fluid and of the acceleration
due to gravity.
For the description of the various phenomena one has made use of

well-known laws of experimental hydraulics. Hence they will only briefly
mentioned in this work with reference to the pertinent author.

In the present paper the author could define by elementary methods
certain minimum conditions for the energy dissipation function of the stream. Omitting the rather long analytical derivation, these conditions
will be given in a very simple analytical form by means of two "experimentally
acceptable" relations. One has also defined certain reference
conditions associated with an "indifferent" particle, i.e. neither settling nor
buoyant in the fluid.

In all the phenomena investigated, be it for a buoyant or settling
particle, for great values of the density ratio (as in the conveyance of a
solid in a gas) and for great values of the volumetric concentration (as in
the conveyance of cylindrical bodies near the size of the pipe), the
developed theory could be verified without finding any conceptual inconsistency
in these extreme cases of hydraulic transport at the limit.

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