Answer:
661284 lb-ft
Explanation:
We are given that height of water tank=18 ft
Radius of circular tank=12 ft
Density of water=[tex]62.4 lb/ft^3[/tex]
[tex]\frac{r}{h}=\frac{12}{18}=\frac{2}{3}[/tex]
[tex]r=\frac{2}{3}h[/tex]
We have to find the work done in pumping all of the water over the top of the tank.
[tex]m=density\times volume [/tex]
[tex]W=m\times distance=62.4\times \pi r^2 (18-h) dh[/tex]
[tex]W=62.4\times 3.14\times \frac{4}{9}h^2(18-h)dh[/tex]
[tex]W=195.936\cdot \int_{0}^{15}(8h^2-\farc{4}{9}h^3dh[/tex]
[tex]W=195.936\times [\frac{8h^3}{3}-\frac{h^4}{9}]^{15}_0[/tex]
[tex]W=195.936\times 3375=661284 ftlb[/tex]
Hence, the work done in pumping all of the water over the top of the tank=661284 ft lb.
