Waec Model Questions Vol1 2023 Agricultural Science Question 34

Using the simplified Rothermel fire‑spread model, the rate of spread R (m min⁻¹) is given by R = (I·ξ) / (ρ_b·ε·Q_ig). The parameters are: heat of combustion I = 18 000 kJ kg⁻¹, heat of ignition Q_ig = 2 500 kJ kg⁻¹. For a flat terrain (scenario A) the wind speed is 5 m s⁻¹, fuel load = 1.2 t ha⁻¹, and fuel moisture = 12 %. For a sloping terrain (scenario B) the wind speed is 3 m s⁻¹, slope = 15°, fuel load = 1.5 t ha⁻¹, and fuel moisture = 8 %. The propagating flux ratio ξ is calculated as ξ = 0.1·(1+0.05·U) for flat ground and ξ = 0.1·(1+0.05·U)·(1+0.03·S) for slope, where U is wind speed (m s⁻¹) and S is slope percent (≈ tan θ·100). Bulk density ρ_b is approximated as fuel load (t ha⁻¹) × 0.1 (kg m⁻³). Effective heating number ε = 0.8 - 0.01·M, where M is moisture (%). Compute the rate of spread for both scenarios and state which scenario spreads faster.