GATE 2023 ES – Question 61
An80 m effective stack emits1200 g/hour CO. The windrose is shown. Dispersion coefficients (σy, σz), in m: Northeast (50, 20); North (45, 30); Northwest (40, 35); East (45, 30); Southeast (55, 35); South (60, 40); Southwest (65, 45); West (70, 50). At the most frequent wind direction, find ground-level plume-centerline concentration2 km downwind in µg/m³. The printed request calls it PM₂.₅.
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Correct answer: 1.75 to 1.95
Explanation
The windrose’s largest frequency is northwest, with wind speed 3 m/s; corresponding σy=40 m,σz=35 m. With ground reflection, the Gaussian ground-centerline formula is $C=Q/(\pi u\sigma_y\sigma_z)e^{-H^2/(2\sigma_z^2)}$. Convert Q to 333333.3 µg/s and substitute to obtain **1.85 µg/m³**. The emission datum is CO but the requested pollutant label says PM₂.₅; this calculation follows the supplied source strength as a passive pollutant and preserves that source-label inconsistency.