The Effect of Stream Flow on
Waste Assimilation Capacity
DONALD J. O'CONNOR, Associate Professor of Civil Engineering
Manhattan College,
New York, N. Y.
It is the purpose of this paper to demonstrate the application of recent
developments to the determination of the pollution capacity of natural
streams, with particular reference to the oxygen balance and the various factors which influence it. Streeter and Phelps (1) first defined the dissolved
oxygen profile of a river subjected to organic pollution. Subsequent work,
both in the field and the laboratory, has indicated the utility, if not the validity, of these formulations. Difficulty, however, has been encountered in
adequately defining the oxidation and reaeration coefficients, particularly as
they are affected by variations in stream flow. Furthermore, the application
of the Streeter-Phelps formula requires an accurate measure of the time of
travel, which is affected by many hydraulic and physical factors. Developments in the past few years have done much to overcome these objections
and to facilitate its practical application of the formulae. The specific objectives of this paper are: (1) to present a modification of the basic formula
which eliminates the time of flow; and (2) to indicate the effect of flow on
the stream coefficients and on the pollution capacity.
PREVIOUS WORK
The basic differential equation defining the oxygen relationship in a
stream subjected to organic pollution is as follows:
#-V K2°
(1)
The first term on the right-hand side of equation (1) represents the rate of
deaeration and the second the rate of reaeration. Both are assumed to proceed
in accordance with first-order kinetics. This assumption for reaeration is
consistent with both theory and data. It is, however, very questionable that
first-order kinetics adequately defines the biochemical reaction. In spite of
the theoretical short-coming, it does provide, empirically, a basis for comparison and a convenience of numerical operation. This first reaction increases the dissolved oxygen deficit at a rate that is proportional to the concentration of organic matter, L. The second reaction, the reaeration,
replenishes the oxygen utilized by the first reaction and decreases the deficit.
K^ and K2 are therefore, respectively, the coefficients of deoxygenation and
and reaeration. The concentration, L, may be related to the location of the
waste discharge by:
L =   L.e
-Krt
(2)
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