# Balancing of domestic hot water systems

​​​​In domestic hot water distribution, temperature of water in the pipes drops significantly when consumption is low or zero. As a result, people get disappointed to wait so long time to obtain hot water when required. Moreover, below 55°C, the bacteria (Legionella) proliferate dangerously.

To keep the water hot, a permanent circulation is maintained in pipes to compensate for heat losses. A circulation pump is therefore installed guaranteeing a minimum flow q1 in the loop (Fig 1) ###### Determination of circulation flows
If we accept the most unfavoured user is supplied at a temperature of ΔT below the water supply temperature ts, we can calculate the minimum circulation flow q1. where:

Pm:     Heat losses in Watt of the supply pipes.
Pipes concerned: ΣL + Σd = [SA+AC+AE] + [db+dc+dd+de].
q1 : In l/h.
The supply pipes are generally insulated.
For a ΔT of 40K between the water and the ambience, the heat losses are situated around 10W/metre, independently of the pipe diameter. This is valid if the thickness of the insulation in mm (λ=0.036) equals 0.7 x external pipe diameter (without insulation).

Obviously the best procedure is normally to make calculation according to the insulation really installed. A much better estimation can be done using the following empirical formula:​ If the distribution is well balanced, a wrong estimation of the total flow does not seem dramatic. If the flow is reduced by 50%, and for a supply water temperature of 60°C, the most unfavoured user will have 51°C instead of 55°C. In this case however, the risk of proliferation of legionella increases.

Hereafter, in the examples, we will consider the following hypothesis: ts = 60°C, tr = 55°C and P = 10 W/metre. Consequently: ​​​

The total flow being known, we have to calculate the flow in each branch. Starting from point S (Fig 1) where the temperature sensor is located, the water temperature at the inlet of ​branch A can be calculated. For the first branch, the pipes heat losses are ZAC = PAC+Pdb+Pdc. So we can calculate successively
the temperatures at the nodes and the required flows as shown hereafter. The flow qAD = q1 – qAB, so we can calculate tD and the second branch as above. This systematic and simple procedure can be used even for complicated systems.

Knowing the flows, the plant can be balanced normally, using the Compensated Method or the TA Balance Method.

For a rough estimation of the pump head, the pressure losses in the supply pipes can be neglected. Considering just the return pipes, we suggest H [kPa]= 10+0,15 (LSE+de) +3 kPa for each balancing valve in series (3 in this example). LSE is the length of the return pipe that we suppose to be equal to the length of the supply pipe.

If LSE+de = 100 metres for example, H = 10+15+9 = 34 kPa. In this formula we consider 10 kPa pressure drop for the exchanger, check valve and accessories and a pressure drop in the return pipes of 0.15 kPa/m.

Considering just the branch AC in figure 1, but with 4 distribution circuits, we can use the above formulas to calculate the flows. These formulas can be translated in another form, more suitable for a systematic calculation. This other form is explained based on an example hereafter.​ Following lengths of pipe (in metres) have been adopted:​ The temperature at the supply of the branch is tA and the expected return temperature is tr. For instance tA = 59°C (considering 1°C loss between S and A in figure 1) and tr = 55°C. For a ΔT= tA- tr = 4K, and heat losses per metre of pipe equals 10 W/m in average, the total flow q1 is:​ These formulas can be extended the same way for more circuits. We have used them to calculate the flows. Calculations of the temperatures are not necessary but are given for information. Let us point out that the last circuit requires 67% of the branch flow while the first circuit requires only 8%. On the contrary, if the distribution is not balanced, the first circuit will receive more flow than the last circuit.
###### Balancing domestic hot water distribution with TA-Therm​ The return of each circuit is provided with a thermostatic valve (TA-Therm) that maintains the return water temperature at an adjustable value. A thermometer may be incorporated in the TA-Therm to measure the temperature obtained. The circulation flows are calculated (See figure 2) to size the return pipes and the pump. For the most remote circuits, the pump head is roughly estimated as follows (for TA-Therm with a Kv=0.3): The highest value of H is adopted.
The Kv of 0.3 given above corresponds with a deviation of 2°C, of the water temperature,
relatively to the set point of the TA-Therm.​