Water streams into a 200 x 150m reservoir via a rectangular conduit measuring 1.5 x 1.25m at a 20kmph velocity. In what duration will the water level rise by 2 meters?
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Answer: D. 96min
Explanation
The volume of water needed to raise the reservoir level by two meters is calculated using its surface dimensions. Equating this required reservoir volume to the volumetric flow rate through the rectangular conduit determines the time needed. Solving the flow equation yields a total duration corresponding to ninety six minutes of continuous pumping time. Volumetric flow rate equals the cross sectional area of a conduit multiplied by the velocity of the flowing fluid. Reservoir capacity expansion is determined by multiplying its surface area by the desired water level height increase. Unit conversion between meters, centimeters, and hours is essential for consistent fluid dynamics calculations.
Seventy six minutes underestimates the duration required to deliver the large volume of water needed for a two meter rise. Eighty minutes fails to account for the exact flow rate and conduit cross sectional area proportions correctly. Ninety minutes is close but underestimates the precise calculated time derived from the volumetric flow equation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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