A spherical tank in a petrochemical plant has a radius of 5m.
Give an expression which, when integrated from y=r to
y=dr ,will give the volume of liquid in the tank where r is
the radius and d is the depth of liquid.
If liquid is entering the tank at a rate of 1500 litres per second and
the depth is 3m how long will it take to fill the tank? Give your
answer in seconds.
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1 answer

The volume of a thin slice of water is the area of the slice times its thickness, dy
At a depth of d, with d<r, we have
the radius of the surface of the water is x = √(r^2y^2)
v = ∫[r,dr] π(r^2y^2) dy
Now you can answer the last part by subtracting the volume from the whole sphere's volume of 4/3 pi * 5^3 and dividing by 1500L/s = 1.5 m^3/s 👍
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Steve
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