- #1
daytripper
- 108
- 1
Firstly, I'd like to quickly note that this isn't a homework problem, but rather a problem that I'm about to make up. I've done Calc IV already but recently my friend asked me for help on a problem involving the drainage of a tank and I got a little stuck in thought. I'd like to re-educate myself on this.
let's say you have a cubic tank (sides = 4 feet). There's a pipe sticking up 1 foot off the top of the cube. The tank is filled up to the 3 foot mark. For these equations, I will be using the variable h to represent the distance from the top of the pipe to the water's surface.
[tex]Work\; =\; \int_{init}^{final}{density\; \cdot \; volume\; \cdot \; dist\; \cdot \; dh}[/tex]
So an infintesimal cross section of this cubic tank would be 16*dh and it would weight 62.4*16*dh. We're moving it a total distance of h (where h varies from 2 to 5).
So then the equation would be:
[tex]Work\; =\; 62.4\cdot 16\int_{2}^{5}{h\; dh}[/tex]
which evaluates to 62.4 * 16 * 10.5 = 10483.2... and I'm not sure which units this would be in.
To me, it seems that I did this problem correctly. I put it here under "coursework questions", as it's a typical problem you'd run into in a calculus class. The thing that's throwing me off is the fact that gravity isn't taken into consideration. I mean.. it requires more work to move something uphill than downhill, right? So why didn't I have to say something along the lines of " + 9.8*62.4*16*10.5" (that was sloppy deduction, but you get the idea).
Also, if someone could help me out with what units this is in, that'd be helpful as well.
Thanks for all the help. I can never say how happy I am this site exists. =]
-DT
Homework Statement
let's say you have a cubic tank (sides = 4 feet). There's a pipe sticking up 1 foot off the top of the cube. The tank is filled up to the 3 foot mark. For these equations, I will be using the variable h to represent the distance from the top of the pipe to the water's surface.
Homework Equations
[tex]Work\; =\; \int_{init}^{final}{density\; \cdot \; volume\; \cdot \; dist\; \cdot \; dh}[/tex]
The Attempt at a Solution
So an infintesimal cross section of this cubic tank would be 16*dh and it would weight 62.4*16*dh. We're moving it a total distance of h (where h varies from 2 to 5).
So then the equation would be:
[tex]Work\; =\; 62.4\cdot 16\int_{2}^{5}{h\; dh}[/tex]
which evaluates to 62.4 * 16 * 10.5 = 10483.2... and I'm not sure which units this would be in.
To me, it seems that I did this problem correctly. I put it here under "coursework questions", as it's a typical problem you'd run into in a calculus class. The thing that's throwing me off is the fact that gravity isn't taken into consideration. I mean.. it requires more work to move something uphill than downhill, right? So why didn't I have to say something along the lines of " + 9.8*62.4*16*10.5" (that was sloppy deduction, but you get the idea).
Also, if someone could help me out with what units this is in, that'd be helpful as well.
Thanks for all the help. I can never say how happy I am this site exists. =]
-DT
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