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.

 

[Moetasim]

I would like to clarify that the force exerted by molasses on the inside of the tank is not dependent on the pressure of air. The force exerted by a fluid on a surface is given by the formula F = ρghA, where ρ is the density of the fluid, g is the acceleration due to gravity, h is the height of the fluid column, and A is the area of the surface. In this case, the total force exerted by the molasses on the inside of the tank can be calculated by multiplying the pressure of the molasses by the area of the tank's base.

Using the given values, we can calculate the height of the molasses column as follows:

h = 87.7 m - 9 m = 78.7 m

Substituting this into the formula, we get:

F = (1630 kg/m3)(9.8 m/s2)(78.7 m)(π(3.37/2 m)2)

= 1.95 x 109 N

Therefore, the total force exerted by the molasses on the inside of the tank before it broke was approximately 1.95 billion Newtons. This is a huge amount of force, which explains the destructive impact of the molasses spill.