Q:Suppose a spherical tank is full of water, calculate the work forced to drainpipe it out completely, if the radius 3ft and also there is a spout the 1ft. (water thickness $62.5 Ilbs/ft^3$)

My solution:

I attract a photo drawing the round laying on the x-axis.

You are watching: Work required to pump water out of a spherical tank

(get a generic cross-sectional slice)

$V_slice = π·r^2·h$

$V_slice = π·r^2·dy$

So, now I have to uncover out what "r" is."r" is the same as the secluded "x" that the equation of a circle.So,

$x^2 + y^2 = 9$

$x = +/-\sqrt9 - y^2$

so,

$V_slice = π·(9 - y^2)·dy$

and for force:

$F_slice = (62.5)·π·(9 - y^2)$

And no displacement, which i think I have wrong.

$displacement = (7 - y)$

Therefore we only combine where over there is water, so limits of integration would selection from 0 to 6.

So altogether:$W = \displaystyle\int_0^6 (62.5)·π·(9-y^2)·(7 - y)dy$

calculus integration
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asked might 6 "17 at 16:07

yreyre
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