Volume of Hot & Cold water required for a known volume and temperature

  1. I've just set a solar thermal array for research for my thesis. I would like to simulate different usage patterns to see how the system performs. I'm doing this using a Arduino with temperature sensors at the top hot the tank and on the cold supply which will then control a motorised valve which will dump hot water based on the usage patterns I set. I'm struggling to work out how to calculate this.

    So for example if I want to dump 50l at 45°C and the hot water store is a 60°C and the coldwater supply is at 10°C.

    I need to work out the volume of hot and cold water required. (and tell the motorised valve to open for a time based on the volume calculated)

    I've been playing around with Q=mcΔT for a couple of day, and think I need to rearrange the equation to give me a ratio of the hot/cold water then calculate the actual volume based on how much I want to dump.

    Can anyone point me in the right direction?
     
  2. jcsd
  3. haruspex

    haruspex 13,605
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    Desired vol = V
    Desired temp = Td
    Hot temp = Th
    Cold temp = Tc
    Vol hot needed = V*(Td-Tc)/(Th-Tc)
    Vol cold needed = V*(Th-Td)/(Th-Tc)
    Is that what you're after?
     
  4. Thanks haruspex!! That works.. I've just tested it experimentally

    Do you know what I should look up to get a better understanding to this as where it was derived?
     
  5. haruspex

    haruspex 13,605
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    Suppose Vol hot needed = Vh and Vol cold needed = Vc.
    V = Vh + Vc
    The resulting temperature will be a weighted average of the two source temperatures:
    Td*V = Th*Vh + Tc*Vc
    Then it's just the standard process of solving two simultaneous equations.
     
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