River water DO mechanics & new DO-sag equation

Abstract

DO modeling by Streeter Phelps equation [1] is most popular method to determine the water quality of a River. To compute DO by Streeter Phelps equation River coefficients k1 and k2 (de-oxidation and re-oxygenation) are required. Determination of these coefficients is tedious because it requires field observation of river velocity and depth over a long period of time at river site. To avoid maximum field work in calculating DO of River water DO Modeling approach is developed by combining Lab analysis of water samples DO with field data, e.g. river velocity and depth. Streeter Phelps (1925) developed the 1st important water quality model describing the BOD-DO relationship in a stream. In their pioneering work the simplest system was considered, in which biodegradable waste is discharged to the stream and consumes oxygen, atmospheric re-aeration being the only source of oxygen. The model is based on complicated solution of differential equation for above process. The equation is derived assuming River coefficients k1 and k2 as exponential function of time variation. The authors have simplified the derivation of DO-Sag equation [4] by replacing the exponential function with a quadratic polynomial. To explain the use of new equation, authors have defined the geometry of DO curve known as ‘River Water DO Mechanics’. Also in this paper, new equation is applied to make ‘Shivnath River water DO Model’ with data taken by the author as part of his Ph. D. research work. The results justify the acceptance of new modified equation for River Water Quality Assessment.