Subtopic: Sources of power on the farm – human, animal, mechanical, electrical, wind, solar and biomass
Question Statement:
A 2 m³ biogas plant is to be operated using cow-dung as feedstock. The cow-dung is mixed with water in proportion of 1:1 (by weight) to form a slurry of density 1090 kg m⁻³. The yield of biogas is 0.036 m³ kg⁻¹ of cow-dung. If the hydraulic retention time is 40 days, volume of the digester of the biogas plant will be ________ m³.
Official Answer Key:
3.90 to 4.20
Step-by-Step Solution & Explanation
Plant rating: gas required = 2 m³ day⁻¹.
Cow-dung needed = 2/0.036 = 55.56 kg day⁻¹.
With 1:1 dung:water, slurry mass = 2 × 55.56 = 111.11 kg day⁻¹.
Slurry volume per day = 111.11/1090 = 0.10194 m³ day⁻¹.
Digester volume = daily slurry volume × HRT = 0.10194 × 40 = 4.08 m³ — within the official range 3.90–4.20.
Common error: forgetting the dilution water, which gives 2.04 m³.
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