A power plant has a stack with a diameter of 2 m and emits gases with a stack exit velocity of 15 m/s and a heat emission rate of 4900 kJ/s. The wind speed is 5 m/s. Stability is neutral. If the stack has a geometric height of 40 m, what is the effective stack height, nearly?
- A40 m
- B60 mCorrect
- C80 m
- D100 m
Solution
Concept
Plume rise (Holland / CPCB formula)
Formula
Δh = (1.5 Vs d + 9.6 × 10⁻³ Qh) / u; Heff = hs + Δh
Step-by-step solution
1. 1.5 Vs d = 1.5 × 15 × 2 = 45. 2. 9.6×10⁻³ × Qh = 9.6×10⁻³ × 4900 = 47. 3. Δh = (45 + 47) / 5 = 18.4 m. 4. Heff = 40 + 18.4 = 58.4 m ≈ 60 m.
Explanation
The effective stack height is the geometric height plus the plume rise caused by exit momentum and buoyancy. With the given data the plume rise is about 18 m, giving nearly 60 m.
Why the other options are wrong
40 m ignores the plume rise. 80 m and 100 m would need a plume rise of 40 m or 60 m.
Shortcut
Heff = hs + Δh; Δh ≈ (momentum + buoyancy)/u.
Common mistake
Forgetting the buoyancy term.
Correct answer: B) 60 m