Answer to Question #190770 in Civil and Environmental Engineering for John Prats

Question #190770

A conical tank is full of water is 16 feet across the top and 12 feet deep. Find the work required to pump all the water to a point 2 feet above the top of the vessel.


1
Expert's answer
2021-05-11T07:24:30-0400



work done = force "\\times distace"

= weight density "\\times distance = mgd = fd"

= "\\rho Vgd"

= "\\int_{a}^{b} \\Delta x dx"


taking a small porting of tank to be cylindrical

v= "\\pi r^2h"

"\\frac{R}{16}= \\frac{12-x}{12}"


R= "\\frac{12-x}{12} \\times 16 = \\frac{48-4x}{3}"

"V= (\\frac {48-4x}{13})^2 \\times \\pi dx"

= "( 256- \\frac{128x}{3}+\\frac{32x^2}{9})\\times \\pi"


"\\Delta = x"

V= "804.24x^2-134.04x^3+11.17x^4"


work done w= "\\rho \\int_{2}^{12} 804.24x^2-134.04x^3+11.17x^4"

w= "1.795\\times 10^7 Nfeet"




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