Mixing Solutions: Problems & Solutions Explained

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Discussion Overview

The discussion revolves around problems related to mixing solutions, specifically focusing on a sample problem involving chlorine concentration in a swimming pool. Participants seek to clarify the setup and solution process for such problems, which involve rates of inflow and outflow of solutions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in understanding how to approach mixing solution problems, noting confusion about variables like X and X/volume.
  • Several participants suggest providing a sample problem to facilitate understanding, with one participant offering a specific example involving a swimming pool and chlorine concentrations.
  • Another participant requests the original poster to share their attempt at solving the problem to identify misunderstandings.
  • A participant outlines a method for setting up the problem, introducing the concept of using a differential equation to model the change in chlorine concentration over time.
  • A reference is made to a previously discussed mixing problem, suggesting it may provide additional insights.

Areas of Agreement / Disagreement

Participants generally agree on the need for a sample problem to clarify the concepts involved. However, there is no consensus on the specific approach to solving the problem, as different methods and setups are suggested.

Contextual Notes

Limitations include the lack of a clear understanding of the original poster's approach and the specific assumptions made in setting up the differential equation. The discussion does not resolve the complexities involved in the problem setup and solution process.

Who May Find This Useful

This discussion may be useful for students struggling with mixing solution problems in mathematics or chemistry, particularly those looking for guidance on setting up and solving related differential equations.

TheLaughingMan
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Can anyone help me out with mixing solution problems, I know its not that hard I just am having trouble understanding what to do. Sometimes its X sometimes its X/volume of the tank. Can anyone explain it to me in a simple way?
 
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If you give us a sample problem maybe we could help break it donw for you?
 
john_in_pdx said:
If you give us a sample problem maybe we could help break it donw for you?
Sample:
A swimming pool whose volume is 10,000 gal contains water that is .01% chlorine. Starting at t=0, city water containing .001% Cl is pumped in at 5 gal/min. The pool water flows out at the same rate. What is the % of chlorine in the pool after 1 hr? When will the pool be .002% Cl ?
 
Can you post an attempt?, it'll figure out what you are not understanding.
 
it seems you don't know how to set up the prob. you need to find y(60).
to do this you let y(t)=the amount of cl in the pool at time t. you need to find an expression for dy/dt.

dy/dt = rate in - rate out

rate in =5 gal / min * .001%

rate out = y(t) / 10000 * 5 gal / min

so dy /dt = (5 gal/min * .001%) - (y(t) / 10000 * 5 gal/ min)

you then find the I.F. and intergrate
 

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