If the tank was full before the accident, what was the net outward force the mol

Question

If the tank was full before the accident, what was the net outward force the molasses exerted on its sides? (Hint: Consider the outward force on a circular ring of the tank wall of width dy and at a depth y below the surface. Integrate to find the total outward force. Assume that before the tank ruptured, the pressure at the surface of the molasses was equal to the air pressure outside the tank.)

On the afternoon of January 15, 1919, an unusually warm day in Boston, a 27.4-m-high, 27.4-m-diameter cylindrical metal tank used for storing molasses ruptured. Molasses flooded into the streets in a 9-m deep stream, killing pedestrians and horses, and knocking down buildings. The molasses had a density of 1600 kg/m3

Explanation / Answer

pressure increases linearly, so average pressure is half way down.

half down is a depth of 13.7m

weight of a cylinder of liquid above that point is the weight of a cylinder of volume 13.7 m³

That is 1600 kg/m³ x 13.7 m³ = 21920 kg. Converting to newtons, that is 21920 x 9.8 = 214816 N.

so average pressure is 214816 Pa or N/m²

Area of walls is 27.4 x 27.4 x = 2358 m²

multiply average pressure by volume to get force
R = 214816 N/m² x 2358 m² = 5.065 e+8 newtons

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