An Experimental Study of the Effect of
Channel Surface Roughness on the
Reaeration Rate Coefficient
WILLIE P. ISAACS, Professor
PRICHA CHULAVACHANA, Student
RAYMOND BOGART, Student
Department of Civil Engineering
New Mexico State University
Las Cruces, New Mexico
INTRODUCTION
The DO required for the stabilization of organic matter in a natural stream is
available from the sources that exist in the river and the waste at the point of
discharge; that available by means of reaeration and that produced by the photosynthetic activity of the green plants. Reaeration is usually the most important factor
in the supply of DO. Streeter and Phelps considered that atmospheric reaeration was
the only source of oxygen for many polluted rivers; and that the only withdrawal
was by micro-organism's exertion of BOD. They proposed the "Sag Equation" as
follows:
klLa -kit       *->* -M
V = ~=-   [10   1  -10   l ] +D 10   l
k2-kj
Where k2 is the reaeration coefficient to the logarithm base ten, k i is the BOD
rate constant, , La is the ultimate first stage BOD, and Da is the oxygen deficit at
time zero. The values of La and Da may be measured but ki and k2 are difficult to
estimate. The value of k i is a characteristic of the waste and is usually assumed to be
equal to the BOD rate constant exerted under laboratory conditions. However, k2 is
a function of conditions in the receiving water. A simple and reliable method of
estimating k2 under all conditions does not presently exist, its development being
hindered by a lack of understanding of the true mechanism of the kinetics of gas
transfer into water.
In 1967, Isaacs (1), using his unique experimental apparatus as an idealized
simulated stream, found the reaeration rate constant, k2, to be directly proportional
to average stream velocity, and inversely proportional to the average stream depth
raised to the 3/2 power. The equation for defining this model is as follows:
D    1'2
Um
k2-0-06339(9T7vr6li^
in which, Dm is the molecular diffusivity of oxygen into water, 3     is the kinetic
viscosity of water, V is the average stream velocity, H is the mean depth of flow, and g
is the gravitational constant.
Atmospheric reaeration was defined by this equation over a wide range of
steady uniform flow conditions in a channel of rectangular cross-section. A single
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