Setup a Differential equation with water tanks
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Setup a Differential equation with water tanks

[From: ] [author: ] [Date: 11-09-28] [Hit: ]
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Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. the tank initially contains 175 liters and 23 liters leak out during the first day.

I would just like to know what is the differential equation I need to setup. Thanks

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Let V(t) represent the volume of water in the tank at time t.

dV/dt = c√(V) for some constant c

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dV/dt = k sqrt (V)

dV/dt * 1 / sqrt(V) = k

[ 1 / sqrt(V) ] dV = [ k ] dt
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