Tank Mixing Problem - Just for Fun if you'd like to spend time on it

In summary, this problem is challenging to do, but if you know how to do it, you can already find the answer.
  • #1
rbzima
84
0
Hey, here's a fun problem many of you would probably enjoy trying. I've done it myself, and it truly is a fun problem to do. Here it is:

We have an initial amount of 800 gallons in a tank at 8:00 in the morning on any particular day. 35% of that 800 gallon solution is acidic. Spigot A is turned on every morning at 8:00 AM, putting 15% acidic solution into the tank. 8:30 AM is when Spigot B at the bottom of the tank is turned on, which drains the tank for customer use.

Both spigots range in the rate at which the liquid is coming in and out of the tank. This range is between 4.0 and 4.5 gallons per minute. Everyday I go to ACME ACID to fill my 40 gallon container at 9:00 AM, and I would like the company to guarantee the range of acidity level in my container.

Therefore, we are looking for the narrowest range of acidity when the 40 gallon container is filled completely.

Secondly, if the attendant at ACME ACID one day measures the tank at 8:20 and discovers there to be 884 gallons in the tank, we are looking for the narrowest range of acidity in the 40 gallon container with this taken into account.

Go Nuts!
 
Physics news on Phys.org
  • #2
rbzima said:
Hey, here's a fun problem many of you would probably enjoy trying. I've done it myself, and it truly is a fun problem to do. Here it is:

We have an initial amount of 800 gallons in a tank at 8:00 in the morning on any particular day. 35% of that 800 gallon solution is acidic. Spigot A is turned on every morning at 8:00 AM, putting 15% acidic solution into the tank. 8:30 AM is when Spigot B at the bottom of the tank is turned on, which drains the tank for customer use.

Both spigots range in the rate at which the liquid is coming in and out of the tank. This range is between 4.0 and 4.5 gallons per minute. Everyday I go to ACME ACID to fill my 40 gallon container at 9:00 AM, and I would like the company to guarantee the range of acidity level in my container.

Therefore, we are looking for the narrowest range of acidity when the 40 gallon container is filled completely.

Secondly, if the attendant at ACME ACID one day measures the tank at 8:20 and discovers there to be 884 gallons in the tank, we are looking for the narrowest range of acidity in the 40 gallon container with this taken into account.

Go Nuts!
You really have to give the posters at this forum a little more credit than that :rolleyes:

Come on, we both know this problem probably isn't very fun for most people who know how to do it, and this is obviously a homework problem, so why don't you go ahead and show some work and where you're stuck if you want assistance.

edit: actually you'd probably be better off putting this in the homework help section
 
Last edited:
  • #3
Actually, I did it last semester and already know the answer, because it was a coursework project. If you'd like, I can send you the entire project right now from last semester. I thought people here might like to try something challenging.

Just a reiteration: THIS IS NOT HOMEWORK OR ANYTHING RELATED TO COURSEWORK DUE THIS SEMESTER. If I knew how to upload the whole thing, I would do so, but it's sad I don't.
 

1. What is the Tank Mixing Problem?

The Tank Mixing Problem is a mathematical puzzle that involves different-sized tanks filled with different amounts of water. The goal is to determine the minimum number of steps required to evenly distribute the water among the tanks.

2. How is the Tank Mixing Problem solved?

The Tank Mixing Problem can be solved using a method called "Gauss-Jordan elimination," which involves creating a matrix and performing row operations to simplify it until a solution is found. There are also online calculators and software programs available that can solve the problem automatically.

3. What is the significance of the Tank Mixing Problem?

The Tank Mixing Problem may seem like a simple puzzle, but it has real-world applications in chemical engineering, where it can be used to determine the optimal way to mix different chemicals in tanks. It also helps develop critical thinking and problem-solving skills.

4. Are there any variations of the Tank Mixing Problem?

Yes, there are several variations of the Tank Mixing Problem, such as using different numbers of tanks, different amounts of water, or adding obstacles that restrict the flow of water between tanks. These variations can make the problem more challenging and require different approaches to solve.

5. Is the Tank Mixing Problem only for fun or does it have practical use?

While the Tank Mixing Problem can be a fun and challenging puzzle, it also has practical use in various fields such as chemistry, engineering, and computer science. It can help optimize processes involving mixing and distribution of liquids, making it a valuable problem to solve.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
3K
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
9
Views
3K
  • Mechanical Engineering
Replies
5
Views
1K
Replies
3
Views
2K
  • General Engineering
Replies
27
Views
8K
Replies
4
Views
8K
  • General Discussion
Replies
8
Views
3K
Replies
64
Views
15K
Back
Top