Question

Design an appropriate size of biogas plant for a family of 6 members owning 2 cows, 2 buffaloes and 2 calves. One candle lamp is used for lighting purpose for 4 hours. (Assumption: dung production by cow, buffalo and calf are 10 kg, 15 kg and 5 kg respectively; cooking requirement is 0.25 m\(^3\) gas per day per person and 0.12 m\(^3\) gas per hour per lamp; gas production 0.04 m\(^3\) per kg of dung)

• A. 1.8 m\(^3\)
• B. 2.0 m\(^3\)
• C. 3.0 m\(^3\)
• D. 2.5 m\(^3\)

Hint:

Biogas plant size is determined by the total gas requirement.
Always calculate both production and consumption.
Choose the size that meets the requirement.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to design the size of a biogas plant based on dung availability and gas requirements.
The plant size is determined by the daily gas production and consumption.

Step 2: Key Formula or Approach:
Total dung available = Sum of dung from all animals.
Total gas production = Dung \(\times\) Gas production per kg dung.
Total gas requirement = Cooking requirement + Lighting requirement.
Plant size = Gas requirement (Gas production per m\(^3\)).

Step 3: Detailed Explanation:
Dung from 2 cows = 2 \(\times\) 10 = 20 kg.
Dung from 2 buffaloes = 2 \(\times\) 15 = 30 kg.
Dung from 2 calves = 2 \(\times\) 5 = 10 kg.
Total dung = 20 + 30 + 10 = 60 kg per day.
Gas production = 60 \(\times\) 0.04 = 2.4 m\(^3\) per day.
Cooking requirement = 6 persons \(\times\) 0.25 = 1.5 m\(^3\) per day.
Lighting requirement = 1 lamp \(\times\) 0.12 \(\times\) 4 hours = 0.48 m\(^3\) per day.
Total gas requirement = 1.5 + 0.48 = 1.98 m\(^3\) per day.
Since gas production (2.4 m\(^3\)) is more than requirement (1.98 m\(^3\)), the plant size is based on production.
Plant size = 2.4 m\(^3\), which is approximately 2.5 m\(^3\).

Step 4: Final Answer:
The appropriate size of biogas plant is 2.5 m\(^3\).
Hence, the correct option is (D).