Water tanks
Water tanks?
Two cylindrical water tanks stand side by side. One has a radius of 4 meters and contains water to a depth of 12.5 meters. The another has a radius of 3 meters and is empty. Water is pumped from the first tank to the second tank at a rate of 10 cubic meters per minute. How long, one-tenth of a minute, the pump must run before the depth of water is the same in both tanks?
The formula for a cylindrical volume is (pi) (radius) ^ 2 (D) what the total volume of water that we are working with is (Vtot) = (pi) (4) ^ 2 (12.5) = 200 (pi) [eq1] The volume of water Tank1 and Tank2 in particular depths, D1 and D2 are (Vtank1) = (Pi) 16 (D1) [EQ2] (Vtank2) = (pi) 9 (D2) [EQ3] We also know that at any given time … (Vtank1) + (Vtank2) = (Vtot) [EQ4] We know the volume Tank2 when the water depth in both tanks are the same, so d1 = d2 = d, and solve equation [EQ4] using [eq1], [EQ2] and [EQ3]: (pi) 16 (d) + (pi) 9 (d) = 200 (pi) 16 (d) + 9 (d) = 200 25d = 200 d = 8 Use [EQ3] determine how water is Tank2 itself when its depth is 8. (Vtank2) = (pi) 9 (8) = 72 (pi) = 226.1952 m ^ 3 If the pump is running at 10 m ^ 3 / min, then Tank2 will 226.1952 m ^ 3 of water in it after 226.1952/10 minutes. Response: 22.6 minutes
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Tags: green, rainwater, sustainability, tanks, water
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