Module 8 : Specialized Traffic Studies

Lecture 43 : Fuel Consumption and Emission Studies

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	Gaussian Dispersion Model This is a simple mathematical model used to estimate the concentration of pollutants at a point at some distance from the source of emission. This model is used for static as well as mobile sources of emissions. In this model, the dispersion in the three dimensions is calculated. Dispersion in the downwind direction is a function of the mean wind speed blowing across the plume. Air pollution is represented by an idealized plume coming from the top of a stack of some height and diameter. The major assumption in this model is that over short periods of time (such as a few hours), steady state conditions exists with regard to air pollutant emissions and meteorological changes. The prominent limitation of this model is that it is not suitable for pollutants which undergo chemical transformations in the atmosphere. Also, it depends largely on steady state meteorological conditions and is short term in nature. The Fig. 1 shows the dispersion of pollutants in a Gaussian plume. Figure 1: Gaussian Dispersion Plume Dispersion in the cross-wind direction and in the vertical direction will be governed by the Gaussian plume equations of lateral dispersion. Lateral dispersion depends on a value known as the atmospheric condition, which is a measure of the relative stability of the surrounding air. The model assumes that dispersion in these two dimensions will take the form of a normal Gaussian curve, with the maximum concentration in the center of the plume. The model maybe used to calculate the Effective Stack Height, Lateral and Vertical Dispersion Coefficients and Ground-Level Concentrations. The Gaussian plume is used to find out the concentration of pollutants at any point in space, and is given by: $$C(x,y,z)=\frac{Q}{2\pi u\sigma_y\sigma_z}\times e^{\frac{-y^2}{2... ...2}{2 \sigma_z^2}\right)}+ e^{\left(\frac{-(z+h)^2}{2\sigma_z^2}\right)}\right)$$ (1) where, $C$ = concentration of the emission (micro grams/cubic meter) at any point $x$ meters downwind of the source, $y$ meters laterally from the centerline of the plume, and $z$ meters above ground level.$Q$ = quantity or mass of the emission (in grams) per unit of time (seconds), $u$ = wind speed (in meters per second), $h$ = height of the source above ground level (in meters), $\sigma y$ and $\sigma z$ are the standard deviations of a statistically normal plume in the lateral and vertical dimensions, respectively. They are functions of $x$. Numerical example A bus stalled at a signal emits pollutants at the rate of 20000g/s. The exhaust pipe is situated at height of 0.75 m from the Ground level. What will be the concentration of pollutants inhaled by a man living on the first floor of a building with storey height 3.5 m? The building is situated at a lateral distance of 5m from the main road and longitudinal distance of 4m downwind of the source. Assume a wind velocity of 10 m/s, $\sigma y$ = 375m and $\sigma z$ = 120m. Solution: The concentration of the emission is given by eqn. 4.2 which is $$C(x,y,z)=\frac{Q}{2\pi u\sigma_y\sigma_z}\times e^{\frac{-y^2}{2... ...2}{2 \sigma_z^2}\right)}+ e^{\left(\frac{-(z+h)^2}{2\sigma_z^2}\right)}\right)$$ Given that, the man lives on the first floor of a building which has a storey height 3.5m. Hence, the man will inhale the pollutants at a distance of 3.5 * 2 = 7m from the ground level. Also given that the exhaust pipe is at a height of 0.75m form the ground and the lateral distance $'y'$ is 5m. The longitudinal distance $'x'$ is 4m. $\sigma y$ and $\sigma z$ are functions of $x$ and are given as 375m and 120m respectively. Substituting the values given, we have, The concentration of the emission, $$C(x, y, z) = \frac{20000}{2 \pi *10*375*120} * exp \frac{-5^2}{2*375^2} * (exp ( \frac{-(7-.5)^2}{2*375^2}) + exp (\frac{-(7+.5)^2}{2*375^2})),$$ which is equal to 0.0141 micro grams per cubic meters.