Introduction / Context:
Fire-fighting water demand is a critical design component in urban water-supply engineering. For simultaneous fires, engineers estimate the required volume by multiplying the number of active streams by their discharge rate and the total duration of operation. This problem checks your ability to convert a practical fire scenario into a clear water quantity estimate.
Given Data / Assumptions:
- Number of simultaneous fires = 4.
- Each fire hydrant operates 3 streams (total streams = 4 * 3).
- Standard discharge per hydrant stream (assumed) = 1,000 L/min per stream (common design convention).
- Duration of each fire = 4 hours = 240 minutes.
- 1 kilolitre (kL) = 1,000 litres (L).
Concept / Approach:
Compute the total volume by first finding the total number of operating streams, then multiply by the discharge per stream and by the duration. Finally, convert litres to kilolitres for reporting. The population figure (40 lakhs) is background context for city size but is not directly used in this specific simultaneous-fire volume calculation.
Step-by-Step Solution:
Total streams, N_streams = number_of_fires * streams_per_fireN_streams = 4 * 3 = 12 streamsDischarge per stream, q = 1,000 L/minDuration, t = 4 hours = 240 minutesTotal discharge rate, Q_total = N_streams * q = 12 * 1,000 = 12,000 L/minTotal volume (litres), V_L = Q_total * t = 12,000 * 240 = 2,880,000 LConvert to kilolitres: V_kL = V_L / 1,000 = 2,880 kL
Verification / Alternative check:
Sanity check: One stream at 1,000 L/min for 240 minutes uses 240,000 L = 240 kL. With 12 streams, 12 * 240 kL = 2,880 kL, which matches the computed value.
Why Other Options Are Wrong:
- 1,880 kL: Underestimates the discharge; would imply a smaller stream flow or fewer streams.
- 3,880 kL and 4,880 kL: Overestimates the requirement relative to the standard 1,000 L/min per stream for 12 streams over 4 hours.
- None of these: Incorrect because 2,880 kL is attainable directly from standard assumptions.
Common Pitfalls:
- Using flow per hydrant instead of per stream; in practice, the specification is per stream from the hydrant.
- Forgetting to convert hours to minutes, or litres to kilolitres.
- Incorrectly multiplying by population; population is used for overall fire-demand design norms, not this specific simultaneous-event volume.
Final Answer:
2,880 kilolitres
Discussion & Comments