Modeling Tools for Environmental Engineers and Scientists

Important assumptions behind these equations are that they are applicable inthe above form only to flat terrains, the pollutant is conservative, and thewind velocity is constant.The effective height of the stack, H, can be found from its physical height,h, and the plume rise, ∆h, by the following equation:H = h + ∆h = h + v sdU 1.5 + 2.68 × 10 –3 p atm. T s – Tatm.T d where v s is the stack gas velocity, d is the stack inside diameter, p atm. and t atm.are the atmospheric pressure and temperature, and T s is the temperature ofthe stack gases. The measured wind velocity, U 0 , at the height of theanemometer, h 0 , may have to be corrected for stack height, h, using thefollowing equation:kU = U 0 hh0where the exponent k is often taken as 1/7.The dispersion coefficients depend on the downwind distances and the stabilityof the atmosphere, and they have to be read off plots. The stability conditionshave to be established based on wind speed and weather conditionsaccording to the following table:Wind SpeedDayNight(m/s) Strong Medium C Cloudy Calm and Clear6 C D D D DAs part of this example, the curve-fitting feature available in MATLAB ®is also illustrated here in transforming the original plots of Pasquill (1962)and Gifford (1976) into equations for integrating into the rest of the model.(Originally, these plots were developed by fitting curves to experimentallymeasured data, which is a standard procedure in analyzing experimental dataand developing mathematical models from physical models as discussed inChapter 1. Here, that process is mimicked by obtaining the “data” off thecharts and re-creating the curves and equations to approximate them.)The MATLAB ® package is used first to develop polynomial equations tocharacterize the stability curves. The equations obtained from this curvefittingexercise are summarized here:s© 2002 by CRC Press LLC