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Thread: Mixtures for brewing coffee (basic mixture model is da/dt= (rate in) - (rate out) )

  1. #1

    Mixtures for brewing coffee (basic mixture model is da/dt= (rate in) - (rate out) )

    I have an interesting question here... For my Diff EQ class, we are doing projects, making mathematical models of different things.

    I am doing a model of brewing coffee, looking specifically at the mixing aspect. I was trying to start by making a basic model, than incorporate temperature, evaporation, etc. Basic mixtures model is:

    da/dt= (rate in) - (rate out)

    This would be the amount of salt (or in this case coffee) remaining per amount of time. I want to find the amount of coffee that comes out when mixed for a set amount of water and coffee. How would I set an equation for this up?

  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by gtrautman View Post
    I have an interesting question here... For my Diff EQ class, we are doing projects, making mathematical models of different things.

    I am doing a model of brewing coffee, looking specifically at the mixing aspect. I was trying to start by making a basic model, than incorporate temperature, evaporation, etc. Basic mixtures model is:

    da/dt= (rate in) - (rate out)

    This would be the amount of salt (or in this case coffee) remaining per amount of time. I want to find the amount of coffee that comes out when mixed for a set amount of water and coffee. How would I set an equation for this up?
    What are your thoughts, based on whatever "salt" examples you've studied? What have you tried? How far have you gotten? Where are you stuck?

    (Also, where else have you posted this question, other than here and on Yahoo? We don't want to waste your time by duplicating what you've already gotten elsewhere. Also, does your instructor allow for portions of this project to be completed by persons outside of the class?)

    Please be complete. Thank you!

  3. #3
    Quote Originally Posted by stapel View Post
    What are your thoughts, based on whatever "salt" examples you've studied? What have you tried? How far have you gotten? Where are you stuck?

    (Also, where else have you posted this question, other than here and on Yahoo? We don't want to waste your time by duplicating what you've already gotten elsewhere. Also, does your instructor allow for portions of this project to be completed by persons outside of the class?)

    Please be complete. Thank you!
    Thanks for getting back. Right now I have just posted it here and on yahoo, but have gotten noting there. She is fine with us getting help with portions from people outside of the class and encouraged it.

    So far I have actually tried using it as a salt mixture using the dA/dt=(rate in) - (rate out), but my problem with this is that it is finding what is left of the "salt". I need to find and equation were I would be adding a pure liquid to the pure salt and see the mixture out in terms of time. I did not know an equation for this though.

    I have now tried looking at it as a chemical reaction where one chemical would be coffee and the other be water and the result be the liquid coffee. I have gotten this to work and have an answer but it still doesn't do exactly what I want. Is there a way to use the result and one of the chemicals to find how much of the other chemical was used? For the project we are really trying to find the coffee to water ratio. Will use a constant amount of water but use the coffee as what we want to find. I cannot figure out how to do this though...

    Any Ideas?

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