Answer to Question #339409 in Calculus for alli

Question

A storage tank is a right circular cylinder 20 ft long and 8 ft in diameter with

its axis horizontal. If the tank is half full of olive oil weighing 57 lb/ft3, find the

work done in emptying it through a pipe that runs from the bottom of the

tank to an outlet that is 6 ft above the top of the tank.

Answer 1

The amount of energy transferred is known as work done. Also one can say that force is required to move the object in the direction of force, i.e.,

$W = F \cdot d$

Work done may be positive, negative or zero, it depends upon the angle between the force and the displacement.

Here, the length of the right circular cylinder is 20 ft.

$W=\int^b_a F(x)dx$

a=-4 ft=-1.2192 m

b=6=1.8288 m

$V=\pi r^2 \Delta x$

r=8/2=4 ft=1.2192 m

$V=1.49\pi\Delta x$

57 lb/fr³=913 kg/m³

$m=Vd=1.49\pi\Delta x 913=1360.4 \pi \Delta x$

$F=mg=1360.4\pi\Delta x 9.8=13331.6 \pi \Delta x$

$W=\int^{1.8288}_{-1.2192}13331.6 \pi dx=13331.6 x|^{1.8288}_{-1.2192}=13331.6 (1.8288+1.2192)=40634.7 J$