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Volume of Hot & Cold water required for a known volume and temperature 
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#1
Jun2512, 05:38 PM

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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
Jun2612, 12:40 AM

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Desired temp = Td Hot temp = Th Cold temp = Tc Vol hot needed = V*(TdTc)/(ThTc) Vol cold needed = V*(ThTd)/(ThTc) Is that what you're after? 


#3
Jun2612, 03:21 AM

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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? 


#4
Jun2612, 04:18 AM

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