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

by jmar71n
Tags: enthalpy change, mixing of water, solar thermal
 P: 2 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?
HW Helper
Thanks
P: 7,948
 Quote by jmar71n 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?
 P: 2 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?
HW Helper
Thanks
P: 7,948

## 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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