Total force by molasses on inside of tank

[shenwei1988]

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?

 

[shenwei1988]

by the way, i am sure if we need to consider the air pressure or not.