## 3 Results
### Hydraulic Pressure and Power Losses in Low-Temperature Systems  
In the previous section it was shown that low-temperature space heaters connected to a closed-loop heat pump could significantly reduce the energy use and CO\({}_{2}\) emission of a single-family dwelling. However, the investigated space heaters in the previous sections were assessed according to current operational practice. The performance of radiator systems were evaluated at a temperature drop of 10 \({}^{\circ}\)C, and floor heating system was assessed at a temperature drop of 5 \({}^{\circ}\)C.  
In this section the effects of smaller temperature drops (high water flow rates) will be thoroughly investigated. It is a well-known fact that water flow rates in low-temperature systems are usually much higher than in high-temperature system. If distribution pipes are not sized properly, this may significantly increase the electrical power required by the circulation pumps. In order to minimize the required pumping power, the inner diameter of each pipe section in a hydronic network must be selected with great care. In the following paragraphs, the influence of increased water flow rate and the inner pipe diameter on the pressure loss and pumping power need is evaluated. From here on in, the inner pipe diameter is referred to as pipe diameter only. Figure 5 compares the increase of hydraulic pressure loss with increased water flow rate for pipe diameters currently used in floor and radiator systems in single-family dwellings. In order to maintain the current design guide value at around 100 Pa/m for hydraulic pressure loss in distribution pipes, pipe diameters of 7.7, 10 and 13 mm are required for water flow rates of 0.01, 0.017 and 0.034 kg/s, respectively. In other words, an increase of pipe diameter from 7.7 to 13 mm (by 69%) would allow an increase water flow rate from 0.01 to 0.034 kg/s (by 240%) without increasing the pipe pressure loss in a circuit. Figure 6 shows the change in ratio between the pumping power need and the heat output with increased water flow rate for a floor heated room of 20 m\({}^{2}\). In accordance with the manufacturers' suggestions, the pipe length, l\({}_{\rm pipe}\), of the underfloor heating circuit and the pump efficiency, \(\eta_{\rm pump}\), were set at 70 m and 25%, respectively [(43; 44)]. The water supply temperature was held at 35 \({}^{\circ}\)C, and water flow rate was increased from initial 0.009 kg/s to 0.05 kg/s. Figure 5: The increase of hydraulic pressure loss with increase of water mass flow rates for three pipe diameters usually used in floor and radiator heating systems. By combining data from Figures 5 and 6, it can be observed that the pumping power need for a pipe diameter of 10 mm is 0.1% of produced heat output at hydraulic pressure loss of 100 Pa/m. By increasing the diameter to 13 mm, the ratio would increase to 0.17% but the water flow rate would increase by 2 times. Even by allowing the pressure loss to increase to 344 Pa/m, the pumping power need would still be about 0.6% of the generated heat output for distribution pipes of 10 mm. It also shows that the pressure loss would be about 195 Pa/m when increasing the diameter to 13 mm and water flow rate to 0.05 kg/s, and that the ratio between the required pumping power and produced heat output would be about 0.5% in that case. However, although it was fully possible to use a water flow of 0.05 kg/s per circuit in floor heating systems, there is no practical justification to go above 0.035 kg/s. According to Table 4, an increase from 0.035 kg/s to 0.05 kg/s per circuit would increase pumping power need by 170% but this increase would only improve Coefficient of Performance (COP) of the considered GSHP by 2%. Figures 5 and 6 clearly show that pumping requirements in hydronic systems can easily be reduced by a proper pipe design. Table 4 also shows that it would be beneficial to use water flow of a high rate in a floor heating system supported by a heat pump.