How can I calculate heat loss in a hot water pipe system?

In summary, the author has done calculations for a 120 liter electric vertical hot water tank with losses based on equation for a two node stratification with an existing 120 liter heater. He wants to know details about the pipe specification and flow rate.
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wolverin
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Hello friends,

I am into modelling of electric hot water tank which is vertical and has the capacity of 120 litres. I just assumed certain charactersitics of an existing heater so as to be more realistic in my approach. Now I am facing certain troubles in my calculations, if you know please help me out with this.

I have done the stratification of my hot water tank with the elementary equations of joules law, heat equation and convection equation so as to know how my temperature vary with stratification. I considered for my heater, a two node stratification with the heating element at the top of the tank. I frammed the equation for the two nodes and got the output for a particular power of 3kW (which is assumed from an existing 120 l heater). Now I would like to know how my output temperature will affected when there are losses.

The output temperature considered for domestic use is 60°C for cleaning purpose and 40°C for drinking and bathing purpose. So I want to frame the losses based on the fact to get this temperature at the taps after the losses has been considered.
My heating range of heater is till 65°C after that I have coded the thermostat to cut the supply.

So now let me explqin the losses:

To my knowledge there are 3 losses in a electric vertical hot water tank:
  1. Storage Losses
  2. Distribution Losses
  3. Generation Losses

So for storage losses: for an existing hot water tank of capacity 120 liters the cooling constant is 0.38 W/litre K day. So I have assumed this constant to my heater as I did not get any equation to support my inference. If you have got any idea about to calculation of storage loss that would be really helpful

Now for distribution losses:

I don't have to get through all the losses like mechanical, I am more concentrated into thermal losses affected my pipe material. I would like to know the pipe specifications used
in a 120 liters heater. SO that I can converge at an idea of framing heat loss per metre of pipe.

I have done calculations based on two formulas which I came thorough the sites that I have reffered.

The first formula I got is for a cylindrical tube of made of copper.
Input details are
Temperature of hot water at the tank : 65°C
Temperaure of Cold water: 20°C ( I have doubt in this whether I should give the outlet of the pipe, I think it is yes... It must be the outlet temperature at the pipe if so it is 60°C/40°C)

Length of the pipe assumed is 5 metres
Outer radius of pipe = 1.8 cm
Inner radius of pipe is 1.6 cm ( I would like to take more realistic values of radius for 120l I don't know whether these values will maximum accuracy in temperature at the outlet(60/40°C)

I would like to know flow through the pipe. In the brouchere of various companies it written specific discharge is for example for which I considered for 120 l it is 22litres/min. So I don't know whether it is flow rate of cold and hot water mixed or only the hot water.

and material used for the pipe is copper (pure) so the thermal conductivity of copper is found to be 400W/mK. I don't know which alloying element is used to make copper pipes. I would like to know more exact values and procedure to frame the losses for distribution.

I have also considered the fact of adopting convection and conduction by consdering thermal resistance in series so as to calculate energy lost per unit length.

So I want to know the details of the specification of pipes used in the given tank of 120 liter capacity so as to calculate the losses and flow rate .

I have missed some points I am always at your availablity

Thank you in advance
 
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Related to How can I calculate heat loss in a hot water pipe system?

1. What is hot water tank modelling?

Hot water tank modelling is the process of creating a mathematical or computational representation of a hot water tank system. This model can be used to simulate and predict the behavior of the tank, such as temperature changes and energy consumption.

2. Why is hot water tank modelling important?

Hot water tank modelling is important because it allows for the optimization of energy usage and cost savings. By accurately predicting the behavior of the tank, adjustments can be made to improve efficiency and reduce energy waste.

3. What factors are typically included in a hot water tank model?

A hot water tank model may include factors such as tank size and shape, insulation levels, heating system efficiency, and water usage patterns. It may also take into account external factors such as weather and ambient temperature.

4. How is a hot water tank model validated?

A hot water tank model can be validated by comparing its predictions to real-world data collected from the actual tank. The model can be adjusted and refined until it accurately reflects the behavior of the tank.

5. Can hot water tank modelling be used for different types of tanks?

Yes, hot water tank modelling can be used for various types of tanks, such as electric, gas, or solar-powered tanks. The model can be adapted to suit the specific characteristics of each type of tank.

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