Analog Computation of the    Dispersion   of
Pollutants in the Delaware Estuary
D. J. O'CONNOR, Associate Professor of Civil Engineering
Civil Engineering Department
Manhattan College
New York, New York
L. L. FALK, Waste Consultant
R. G. E. FRANKS, Computer Consultant
Engineering Service Division, Engineering Department
E. I. du Pont de Nemours and Co., Inc.
Wilmington, Delaware
INTRODUCTION
The pollution capacity of estuaries depends on many inter-related factors,
such as fresh-water discharge, longitudinal dispersion, advection, and the characteristic reaction rates. This paper describes a study in which the analog computer was used to investigate certain aspects of the estuarine dispersion problem.
Several investigators have proposed equations describing the concentration
profiles in estuaries (1,2, 3,4). Unfortunately, the solution of many of these equations has required simplifying assumptions that may be invalid for the actual estuary under study. Such assumptions have been made in the domains of both time
and space, such as the steady state condition, constant values of cross-sectional
area, fresh-water discharge, and eddy diffusion coefficients. Solution by modern
computers offers many advantages in this regard, in addition to speed and accuracy. The application of analog computers to the solution of many equations defining pollution patterns has been discussed (5). The analog program in this study
simulated the Fickian mathematical model for estuarine dispersion and took into
account that the cross-sectional area, fresh-water flow, and longitudinal eddy diffusion coefficient varied with distance along the estuary. The solutions were compared with dye distribution data observed (6) in the Delaware River hydraulic model
at Vicksburg, Mississippi.
MATHEMATICAL MODEL
Material released into an estuary disperses due to tidal motion and velocity
gradients and moves down river because of advective effects of fresh-water discharges into the estuary. If the material is non-conservative, its mass also decreases in a manner characteristic of the particular substance. Diffusion can occur
horizontally, vertically, and longitudinally. If the concentration of material is
uniform in the vertical and lateral planes, only the longitudinal diffusion need be
considered. The plane of the segment is perpendicular to the direction of tidal
flow. The equation to describe the time rate-of-change of concentration along
the longitudinal axis of the estuary is:
tca_l_ 9   (EA 9c) - U 9c - Kc
t    A &x Qx dx (1)
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