Question

a rectangular water tank has a length 20 ft, width 10 ft , and depth 15 ft . if the tank is full , how much work does it take to pump all the water out (using calculus)

Answer 1

so this is another combination of mathematical calculus and the physical energy problem.

Answer 2

this one is much easier than the previous one, don't you think so? because there's no dripping water here~! :)

Answer 3

but im still confused

Answer 4

this is what i got 62.4(density of water)(200,the volume) integral 15-h limit 15 to zero

Answer 5

the measurement is ft , not meter.

Answer 6

i know that why u use 62.4 as the density

Answer 7

youd better change to ISU, more convenient to calculate, as 1 g/cm^3 the density of the water/

Answer 8

im sorry i had to go to bed, its midnight here

Answer 9

oh okay thank you for ur help

Answer 10

anwar di u think u can help me

Answer 11

Is the water leaving the tank from the top or the bottom? I'll assume it's leaving from the bottom.

W = F * d; draw the tank with the dimensions. Find the density of an infinitely thin "slab" of water. Its volume is going to be 20*10*dy = 200dy. The force is going to be the volume times the density, so 200dy * 62.4 = 12480dy. The distance that this slab is going to have to travel to leave the tank is y, so the work done in moving that slab is 12480ydy. Sum all the work done by all the slabs with...

\[\int\limits_{0}^{15}12480ydy\]

I got 1404000 foot-pounds of work.

Answer 12

thank u for coming to the rescue , but the answer is 220,500 ft lb

Answer 13

Integrate 12480ydy from 0 to 15 is what I meant to say...

Answer 14

is the distance 15-y

Answer 15

The distance would be 15 - y if the water was leaving from the top... I don't think that wouldn't get the amount of work to be 220500, though...

Answer 16

it just says how much work would it take to pump the water, it doesn"t say top and bottom

Answer 17

Well, for water to be pumped out of a tank it needs to be pumped out from somewhere. The water needs to move to a part of the tank to be pumped out.

Answer 18

here what I have, I am not sure about it though.. haven't done physics in a while:
we have the following formula:
\[W=\int\limits_{v_i}^{v_f}pdv\]
where p is pressure of water (can be found known depth and temperature of water),
vi and vf are the initial and final volume respectively (both known)

Answer 19

knowing depth..*

Answer 20

so it doesn't matter if we use y or 15-y to represent the distance

Answer 21

well we have the initial volume=20*10*15,
final volume=0..
we will get a negative result for the work.

Answer 22

if we use 15-y?

Answer 23

hey im a little confused. can someone please explain to me how the distance become 15-y

Answer 24

I have no idea why my answer is incorrect. If you draw the height of the tank and pick an arbitary point along the height, the distance between the top of the tank and that point is 15 - y.

Answer 25

and when is it just y

Answer 26

Distance betwen the arbitary point and the bottom of the tank.

Answer 27

but in the triangle is the top is just y, and the bottom is 15-y

Answer 28

Triangle?

Answer 29

this is another question , when u slice a triangle and want to use similar triangles the top portion is y and the bottom half is 15-y ,( this just an example)

Answer 30

Yes, I suppose you could think of it that way if you positioned the tank such that the x-axis was the top of the tank and 15 feet below that is the bottom of the tank.

Answer 31

k ty

Answer 32

hey i have a question can i ask