Calculating hot and cold water volumes for mixing to 45°C

[jmar71n]

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?

 

[haruspex]

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.

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?

 

[jmar71n]

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?

 

[haruspex]

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.