Total force by molasses on inside of tank

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The discussion centers on calculating the total force exerted by molasses on the inside of a cylindrical tank before it ruptured in Boston in 1919. The tank's dimensions are given as 87.7 m high and 3.37 m in diameter, with molasses having a density of 1630 kg/m³. The user proposes using integration to account for the varying pressure at different heights within the tank, leading to the equation F=ϕπdH+(ρgπdH²)/2. There is uncertainty regarding whether to include atmospheric pressure in the calculations. The overall goal is to determine the total force exerted by the molasses before the tank broke.
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Homework Statement


On January 15, 1919, a cylindrical tank of molasses ruptured, and poured out over the streets of Boston in a 9 m deep stream. Pedestrians and horses were killed, and buildings were knocked down.

Suppose the tank was 87.7 m high and 3.37 m diameter, and it was full of molasses (density 1630 kg/m3). Find the total force exerted by the molasses on the inside of the tank before it broke.



Homework Equations


P=F/A
P=ρgh
pressure of air 1.103x10^5 use Greek letter ϕ
A is the area
ρ is density
d is diameter

The Attempt at a Solution



since the pressure changes, i think i should integrate to find force.

ΔF=P∙ΔA=∫(ϕ+ρgh)πd∙Δh

after integrate i get : F=ϕπdH+(ρgπdH^2)/2

it's right?
 
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by the way, i am sure if we need to consider the air pressure or not.
 
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