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

In summary, the individual is conducting research for their thesis by using a solar thermal array and an Arduino to simulate various usage patterns. They are struggling to calculate the volume of hot and cold water needed and how long the motorised valve should be open based on their desired temperature and the temperatures of the hot water store and cold water supply. They have been playing around with the equation Q=mcΔT and are looking for further resources to better understand its derivation. They have received helpful guidance on calculating the volume of hot and cold water needed and the resulting temperature.
  • #1
jmar71n
2
0
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?
 
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  • #2
jmar71n said:
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?
 
  • #3
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
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.
 
  • #5


I would approach this problem by using the principles of thermodynamics and fluid dynamics. First, I would calculate the heat energy required to raise the temperature of 50 liters of water from 10°C to 45°C using the equation Q=mcΔT, where Q is the heat energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the temperature difference.

Next, I would determine the volume of hot water needed to provide this amount of heat energy. This can be calculated by dividing the heat energy by the specific heat capacity of hot water (assuming it is the same as regular water) and the temperature difference between the hot water supply and the desired temperature (60°C - 45°C). This will give you the volume of hot water needed to raise the temperature of 50 liters of cold water to 45°C.

To determine the volume of cold water needed, I would use the same equation but with a temperature difference of 10°C - 45°C, as this is the temperature difference between the cold water supply and the desired temperature. This will give you the volume of cold water needed to mix with the hot water to reach the desired temperature.

Once you have calculated the volumes of hot and cold water needed, you can program the motorized valve to open for a specific amount of time based on the flow rate of the valve and the calculated volumes of water. This will allow you to simulate different usage patterns and see how the system performs.

I hope this helps in your research and good luck with your thesis! It's great to see scientists using technology like Arduino to further their studies in renewable energy.
 

1. What is the formula for calculating the volume of hot and cold water needed for a known volume and temperature?

The formula for calculating the volume of hot and cold water needed is: V1 x (T2 - T1) = V2 x (T1 - T3), where V1 is the known volume, T1 is the initial temperature, T2 is the desired final temperature, V2 is the volume of the hot water needed, and T3 is the temperature of the cold water.

2. How do I determine the temperature of the cold water needed for a specific volume and temperature of hot water?

To determine the temperature of the cold water needed, you can rearrange the formula to T3 = (V1 x T1 + V2 x T2) / (V1 + V2). This will give you the temperature of the cold water that, when combined with the hot water, will result in the desired final temperature.

3. Can this formula be used for any type of liquid?

Yes, this formula can be used for any type of liquid as long as the specific heat capacities of the liquids are known. The specific heat capacity is a measure of how much energy is required to raise the temperature of a substance by one degree.

4. What units should be used for the volume and temperature in this formula?

The volume can be in any unit of volume, such as liters or gallons. The temperature should be in degrees Celsius or degrees Fahrenheit, depending on the specific heat capacity of the liquid being used.

5. Are there any other factors that should be considered when using this formula?

Yes, there are a few other factors that should be considered, such as the heat loss or gain during the mixing process, the efficiency of the heating source, and any temperature changes due to atmospheric pressure. These factors may affect the accuracy of the calculated results and should be taken into account when using the formula.

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