An Experimental Study of the Effects of
Stream Channel Cross-Sectional
Geometry on the Reaeration Rate Coefficient
WILLIE P. ISAACS, Professor
MELVIN R. McCORKLE, Graduate Student
WILLIAM F. LORANG, Graduate Student
Department of Civil Engineering
New Mexico State University
Las Cruces, New Mexico
INTRODUCTION
There have been five theoretical or semi-theoretical developments defining the
mass-trasnfer process of diffusion of slightly soluble gases into turbulent liquid systems. Whitman and Lewis (1,2) presented what is probably the most generally used
and most agrumentative explanation of this absorption phenomenon in their so-
called "two film theory". Higbie (3) proposed a model of gas transfer known as the
"penetration theory". Danckwerts (4) presented what is known as the "surface renewal theory". O'Connor and Dobbins (5) extended the Danckwert's theory along
with some simplifying assumptions to a model which they interpreted as defining
natural stream reaeration conditions. Dobbins (6) proposed a theory based upon an
interfacial liquid film that maintains its existence only in a statistical sense. This
model combines the film concept of Whitman and Lewis and the random mixing
concept of Danckwerts. All of these models have been based upon mechanistic
theories which have never been proven experimentally as applying to the reaeration
characteristics of a natural stream.
Churchill, et al., (7) reported on an extensive field study of selected stream
reaches in the Tennessee Valley Authority Area, where great care could be exercised
over the control of stream flow conditions in stream reaches situated below dam
sites. This study is reported by others to be the best effort made toward gathering
field data on stream reaeration rates. The group developed several empirical reaeration formulas which can be used to predict the rate at which oxygen will be absorbed
by water flowing in natural stream channels.
Isaacs and Gaudy (8) reported on a study utilizing an experimental laboratory
apparatus. The reaeration rate coefficient, k2, was found to be directly proportional
to average stream velocity, and inversely proportional to the average stream depth
raised to the 3/2 power. Their proposed model for the reaeration rate coefficient is
defined by a dimensionally homeogenous equation. It is the only equation proposed
thus far which explains the presently recommended variation of k2 with temperature
(9). When tested on the natural stream data reported by Churchill, et al., (7) it
predicted the field measured value of k2 for the thirty reported stream reaches with a
multiple correlation coefficient of 0.95.
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