Full Density
The tank shown below is full of water. Using the fact that the density of water is 1000kg/m^3 find the work (i?
The tank shown below is full of water. Using the fact that the density of water is 1000kg/m^3 find the work (in joules) required to pump the water out of the outlet. Make sure your answer is correct to within one thousand joules.
http://hw.math.ucsb.edu/webwork/math3b-02-W10/tmp/gif/Feb12010-prob7-prob6_4_21.gif
total amount of water to pump = 0.5 width x depth x length = .5 × 3 × 3 × 8 = 36 m³; but,
the distance to pump, h, increases as liquid is drawn out, and the amount at this distance, ΔV, decreases as liquid is drawn out because width decreases linearly with height.
for a given value of h,
width = 3 - (h-2)
depth = 3 - (h-2)
remaining amount to pump = V = .5 (3-(h-2))² × 8;
V = 4 (5-h)²
for a given Δh, write an expression for ΔV, and write an expression for ΔE:
limit as Δh->0: ΔV/Δh = -8(5-h)
dE = k h dV = k h ( -8(5-h)) dh
= k (8h² -40h) dh
where k is amount of energy to pump 1000 kg up 1 m
E(h) = integrate from h=2 to h=5: k( 8h² -40h) dh
=|E(5)-E(2)|
=|k( 8(5)³/3 -20(5)² - (8(2)³/3 -20(2)² ))|
= 108k
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