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Math Help - Need help please with percentages, etc... for this real life Application

  1. #1
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    Need help please with percentages, etc... for this real life Application

    I have a solar hot water collector that puts out water at a very scalding 160 f . directly into the house hot water line ; My ideal water temperature for a shower is 95 f . If i mix in cooler water from my showers cold water faucet which delivers 75 f. during summer months , what percentage of Collector water (160 f) do I need to achieve a 95 f. shower ? If you would, please give me the mathematical formula by plugging in the values listed for the answer. I do appreciate it. Thanks, David.
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  2. #2
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    Re: Need help please with percentages, etc... for this real life Application

    Quote Originally Posted by TheyCallMeDave View Post
    I have a solar hot water collector that puts out water at a very scalding 160 f . directly into the house hot water line ; My ideal water temperature for a shower is 95 f . If i mix in cooler water from my showers cold water faucet which delivers 75 f. during summer months , what percentage of Collector water (160 f) do I need to achieve a 95 f. shower ? If you would, please give me the mathematical formula by plugging in the values listed for the answer. I do appreciate it. Thanks, David.
    1. The energy from the hot water is completely taken by the cold water:
    m_h = mass of hot water
    m_c = mass of cold water

    2.
    m_h(160-95)=m_c(95-75)~\implies~\dfrac{m_h}{m_c}=\dfrac{20}{65}

    3. With 20 (liters, gallons, ...) of hot water and 65 (liters, gallons, ...) of cold water you'll get 85 (liters, gallons, ...) of water with the ideal temperature.
    Last edited by earboth; July 29th 2011 at 10:45 PM.
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  3. #3
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    Re: Need help please with percentages, etc... for this real life Application

    Hi Dave,
    I had a similar problem with a shower. My wife had a hard time adjusting temp so I installed a mixing valve and the hot water is controlled by the mix valve
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