WORK pumping water out of a cylindrical tank.

[Brain0991]

How much work is needed to pump all water out of a cylindrical tank with height of 10 feet, radius 5 feet. Water is pumped to an outflow pipe that is 15 feet above the bottom of the tank.

V = ?r[sup:rkl072zl]2[/sup:rkl072zl]h
V = ?*25*10
V = 250? or 785.4

it doesnt specif the weight of water, but it is 62.4 pounds per cubic foot.

 

[galactus]

Force to move the kth layer is \(\displaystyle ({\pi}r^{2}{\Delta}_{k})\cdot [\text{weight density of water}]=25{\pi}\cdot 62.4{\Delta}x_{k}\)

Distance = \(\displaystyle 15-x_{k}\)

\(\displaystyle \text{Work=Distance*Force}\)

The water is 10 feet deep, so the limits of integration are 0 to 10.

Can you set it up now?.

 

[Brain0991]

work = distance*force
= (15 - x[sub:1wvrfxuk]k[/sub:1wvrfxuk])(25?*62.4)dx[sub:1wvrfxuk]k[/sub:1wvrfxuk]
=the integral from 0 to 10 of (73513.27 - 4900x[sub:1wvrfxuk]k[/sub:1wvrfxuk])dx[sub:1wvrfxuk]k[/sub:1wvrfxuk] ??

 

[galactus]

\(\displaystyle 1560{\pi}\int_{0}^{10}(15-x)dx\)