Tank Drainage Work Calculation

In summary, the conversation discusses a problem involving the drainage of a tank and the calculation of work using calculus. The problem involves a cubic tank filled up to the 3 foot mark with a pipe sticking up 1 foot above the cube. The equations used include the variable h to represent the distance from the top of the pipe to the water's surface. The solution involves finding the work by moving an infintesimal cross section of the tank a total distance of h. The units of the final answer are in force*length, which can be converted to joules or lb*ft. The conversation also addresses the role of gravity in the calculation and its units.
  • #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.

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
 
Last edited:
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  • #2
That looks just fine. You questions about it are tied in with not knowing the units. The 62.4 is lbs/ft^3 or force/volume (the force per cubic foot for water on the earth). The 'g' is already built in. The other way do this with a visible 'g' in metric units is writing g*rho as the constant out front, where g=9.8m/s^2 and rho is the mass density of water 1000 kg/m^3. If you multiply those together you get units of (kg*m/s^2)/m^3. Since kg*m/s^2 is a Newton, the metric force unit, then g*rho is again a force/volume. If you continue on, the rest of the calculation has units of volume*length. So, (force/volume)*(volume*length)=force*length. A Newton*meter=joule. The unit of work. Or lb*ft in the daft unit system.
 

1. What is "Work for Tank Drainage Review"?

"Work for Tank Drainage Review" refers to the process of evaluating and improving the drainage system of a tank, typically used for storing liquids. This can include inspecting the tank, identifying any issues or areas for improvement, and implementing solutions to ensure efficient drainage.

2. Why is it important to conduct a tank drainage review?

A tank drainage review is important because it helps to identify and address any potential issues with the drainage system, such as clogs or leaks. This can prevent problems such as overflow, contamination, and structural damage, which can be costly and dangerous.

3. What are the steps involved in a tank drainage review?

The steps involved in a tank drainage review may vary depending on the specific tank and its drainage system. However, some common steps may include inspecting the tank and its components, testing the drainage system, identifying any issues, and implementing solutions such as cleaning or repairs.

4. Who typically conducts a tank drainage review?

A tank drainage review is typically conducted by a qualified engineer or technician with experience in tank maintenance and drainage systems. It may also involve collaboration with other professionals, such as environmental consultants or safety specialists.

5. How often should a tank drainage review be conducted?

The frequency of tank drainage reviews may vary depending on factors such as the type of tank, its usage, and the environment it is located in. Generally, it is recommended to conduct a review at least once a year, but more frequent reviews may be necessary for tanks with high usage or in harsh environments.

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