The following tank is filled with water. We are going to determine the work required to remove the water out from the top. The dimensions of the tank are w = 12 ft, l = 6 ft and h = 20 ft. The weight density of water is 8 = 62.4 lbs/ ft° X = h d; X = 0 This problem is dependent on the vertical coordinate system to the left. ;th The force, Fi, of the i" layer of water = weight of the i" layer of water = 8 · vi, %3D th where vi = volume of the in layer of water. For this problem, F; lbs The distance, di, we are moving the in ;th layer of water is
The following tank is filled with water. We are going to determine the work required to remove the water out from the top. The dimensions of the tank are w = 12 ft, l = 6 ft and h = 20 ft. The weight density of water is 8 = 62.4 lbs/ ft° X = h d; X = 0 This problem is dependent on the vertical coordinate system to the left. ;th The force, Fi, of the i" layer of water = weight of the i" layer of water = 8 · vi, %3D th where vi = volume of the in layer of water. For this problem, F; lbs The distance, di, we are moving the in ;th layer of water is
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Transcribed Image Text:The following tank is filled with water. We are
going to determine
the work required to remove the water out from
the top.
The dimensions of the tank are
12 ft, l = 6 ft and h = 20 ft.
W =
The weight density of water is 8 = .
62.4 lbs/ft.
X = h
d;
X; IAx
X = 0
This problem is dependent on the vertical
coordinate system to the left.
th
The force, F;, of the i
" layer of water = weight
th
of the in layer of water = 8 · vi,
th
where vi =
volume of the i" layer of water.
For this problem,
Fi
8 .
lbs
The distance, di, we are moving the i" layer of
water is
(must be relate back to r.
Transcribed Image Text:This problem is dependent on the vertical
coordinate system to the left.
th
The force, Fi, of the i" layer of water = weight
th
of the i" layer of water = 8 · Vi,
volume of the i
;th
where vi =
For this problem,
layer of water.
F; = 8 .
lbs
The distance, di, we are moving the i" layer of
;th
water is
(must be relate back to x;)
di
ft
The work required to remove the in
water is wi = F; · di. (Dont forget 8)
layer of
Wi =
ft-lbs
Adding up the work on all the subintervals and
allowing n → ∞, where n represents the
number of
subintervals, gives the integral for total work,
w, required to remove the water from the top.
20
W =
dx
Evaluating the integral yields the total work
W =
ft-lbs
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