Solve ODE Mixture Question: 100 Gal Water Tank

In summary, the conversation discusses a tank with 100 gallons of pure water, where at time = 0, a sugar/water mixture with .2 lbs of sugar per gallon enters at a rate of 3 gallons per minute. The drain at the bottom allows the solution to leave at a rate of 3 gallons per minute, and perfect mixing occurs. The conversation then goes on to discuss the rate of change of sugar content over time, with a given integrating factor. The question is posed of what the sugar content will be after 20 minutes, with the conversation ending on a disagreement over the calculated value.
  • #1
cue928
130
0
Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs.

I show the following:
Rate in: .2 x 3 = .6
Rate out: x/100
Volume: 100

dA/dt = .6 - A/100; I get an integrating factor of e^x/100. It asks what will the sugar content be after 20 minutes. I came up with a C value of 19.4. I get 16.##, they get 9.0348. Any idea where I'm going wrong?
 
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  • #2
hi cue928! :smile:
cue928 said:
Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs.
…
dA/dt = .6 - A/100

oooh :cry: … what happened to the (second) 3 gal per minute? :redface:
 

1. How do I solve an ODE mixture question for a 100 gallon water tank?

To solve an ODE mixture question for a 100 gallon water tank, you will need to use the basic equation: dV/dt = Qin - Qout, where dV/dt represents the change in volume over time, Qin represents the inflow rate, and Qout represents the outflow rate. You will also need to consider any additional factors, such as mixing or evaporation, that may affect the volume of the tank.

2. What is the appropriate initial condition for a 100 gallon water tank ODE mixture question?

The appropriate initial condition for a 100 gallon water tank ODE mixture question will depend on the specific problem you are trying to solve. In general, the initial condition will be the volume of water in the tank at time t=0. This could be 0 gallons if the tank is initially empty, or it could be a specific amount if the tank is already partially filled.

3. How do I determine the inflow and outflow rates for a 100 gallon water tank ODE mixture question?

The inflow and outflow rates for a 100 gallon water tank ODE mixture question will also depend on the specific problem. In most cases, the inflow rate will be a constant value, such as a specified flow rate from a faucet. The outflow rate may also be a constant value, or it could vary based on the volume of water in the tank, for example if the outflow is through a drain that is partially blocked.

4. Can I use different units for the volume and time in a 100 gallon water tank ODE mixture question?

Yes, you can use different units for the volume and time in a 100 gallon water tank ODE mixture question. However, it is important to make sure that the units are consistent throughout the equation. For example, if the volume is given in gallons and the time is given in minutes, the inflow and outflow rates should also be in gallons per minute.

5. How can I check if my solution to a 100 gallon water tank ODE mixture question is correct?

To check if your solution to a 100 gallon water tank ODE mixture question is correct, you can plug your solution into the original equation and see if it satisfies the equation. You can also graph your solution to visually see if it makes sense and captures the behavior of the system. Additionally, you can compare your solution to other known solutions or use software to verify your solution.

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