Water Reserve Decision
At a forward base, three bulk water tanks supply a detachment of 140 personnel. Tank A holds 12,000 L and is 78% full; Tank B holds 8,500 L and is 92% full; Tank C holds 5,400 L and is full. Daily consumption is 2,650 L. A leak on Tank B's outlet loses 0.8 L per minute and cannot be repaired before the next convoy, which is due in exactly 5 days. The commander requires a reserve of at least 10% of the five-day demand to remain at the end of day 5. A repair team could reach the leak in 4 hours, stop the loss completely, but its detour and equipment would consume 300 L of stored water. The logistics officer must decide whether to authorise the repair and whether the base needs to ration before the convoy arrives. All tanks are cylindrical and their stated capacities are usable; ignore evaporation and testing losses.
1. Calculate the total usable water now and the projected five-day demand including the leak. Is the commander's 10% reserve met without rationing?
Read the worked answer
Usable water now:
- Tank A: 12,000 x 0.78 = 9,360 L
- Tank B: 8,500 x 0.92 = 7,820 L
- Tank C: 5,400 L
- Total = 9,360 + 7,820 + 5,400 = 22,580 L
Leak rate: 0.8 L/min x 60 x 24 = 1,152 L/day. Over 5 days: 1,152 x 5 = 5,760 L.
Consumption over 5 days: 2,650 x 5 = 13,250 L. Total demand including leak = 13,250 + 5,760 = 19,010 L.
Remaining at day 5 = 22,580 - 19,010 = 3,570 L. 10% of five-day demand = 0.10 x 19,010 = 1,901 L.
Since 3,570 L is greater than 1,901 L, the reserve is met without rationing. The margin is 3,570 - 1,901 = 1,669 L above the minimum reserve.
2. If the repair is authorised at the start of the period, what is the net water position at day 5, and is the reserve still met?
Read the worked answer
The repair stops the leak after 4 hours, but water is still lost during those 4 hours: 0.8 L/min x 240 min = 192 L. The repair itself consumes 300 L.
Consumption over 5 days remains 13,250 L. Total demand becomes: 13,250 + 192 + 300 = 13,742 L.
Remaining at day 5 = 22,580 - 13,742 = 8,838 L.
The reserve requirement is still 1,901 L, so the reserve is easily met. Compared with no repair, the saving is: 5,760 - (192 + 300) = 5,268 L.
Authorising the repair is clearly worthwhile on water alone, provided the repair team's other risks are acceptable.
3. A crew then draws 1,200 L from Tank B. What percentage of Tank B's capacity remains, and what fraction of the total usable water is now in Tank B?
Read the worked answer
Tank B usable before the draw = 7,820 L. After drawing 1,200 L: 7,820 - 1,200 = 6,620 L.
As a percentage of Tank B's 8,500 L capacity: 6,620 / 8,500 = 0.7788, or about 77.9%.
New total usable water: 9,360 + 6,620 + 5,400 = 21,380 L.
Tank B's share: 6,620 / 21,380 = 0.3096, or about 31.0%.
So Tank B still holds nearly 78% of its own capacity but only about 31% of the base's usable water.