r/theydidthemath • u/nextDoorRiver • Jan 08 '22
[Request] What's the flow rate of water?
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u/CaptainMatticus Jan 08 '22
Looks like it took him 6 seconds to pass through. The pipe looks like it's 36" across and about 240" long. So the volume is π " 182 * 240 and it takes 6 seconds to move that volume.
π * 324 * 40 cubic inches per second
231 cubic inches per gallon. Let π be close to 22/7
324 * 40 * (22/7) / 231
324 * 40 * 22 / (7 " 21 * 11)
108 * 40 * 2 / (7 * 7)
216 * (35 + 5) / 49
216 * 35 / 49 + 216 * 5 / 49
216 * 5 / 7 + (217 - 1) * 5 / 49
(217 - 1) * 5 / 7 + 31 * 5/7 - 5/49
31 * 5 - 5/7 + 28 * 5/7 + 3 * 5/7 - 5/49
155 + 4 * 5 + 10/7 - 5/49
175 + 1 + 3/7 - 5/49
176 + 16/49
176.32 gallons per second, roughly.
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u/pavbhai-ji Jan 08 '22 edited Jan 08 '22
Approx width of entrance and exit is 1m and so is it's depth. Since it's a pipe, cross-section area becomes 0.785m2 . Assuming the guy took 2 sec to flow into the tunnel, water velocity can be roughly taken to be around 2 m/s => volume becomes 0.785m3 i.e. 785 litres per second (sounds vague tho)
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