Pipe dimensioning for heat networks in nPro

On this page you will learn how to dimension pipe diameters of heating networks, cooling networks and 5th generation district heating and cooling (5GDHC) networks using the nPro tool.

Pipe sizing and dimensioning in nPro

In the nPro tool, pipe diameters for district heating networks can be calculated precisely already in the early planning phase. Visualization takes place directly in the map view, see Figure 1.

Figure 1: Pipe diameter sizing and visualization in nPro

Pressure loss calculation

The pressure loss in the pipe network is calculated using the Darcy-Weisbach equation, which relates the pressure gradient to flow velocity, pipe diameter, and friction factor:

\frac{\Delta p}{L} = \lambda \cdot \frac{\rho}{2} \cdot \frac{v^2}{d}

where $\lambda$ is the friction factor, $\rho$ the density of the fluid, $v$ the flow velocity, and $d$ the pipe diameter.

Friction factor

The friction factor $\lambda$ depends on the flow regime, which is determined by the Reynolds number:

Re = \frac{d \cdot v \cdot \rho}{\mu}

with $\mu$ as the dynamic viscosity of the fluid.

Laminar flow ( $Re < 2300$ ):

\lambda = \frac{64}{Re}

Turbulent flow ( $Re \geq 2300$ ): the friction factor is determined iteratively using the Colebrook-White equation:

\frac{1}{\sqrt{\lambda}} = -2 \cdot \log_{10}\left(\frac{\varepsilon}{3.72 \cdot d} + \frac{2.51}{Re \cdot \sqrt{\lambda}}\right)

where $\varepsilon$ is the pipe roughness.

Validation of the pressure loss and diameter calculation

The calculation methods in nPro were compared and validated with different hydraulic calculation tools. As an example, Tables 1 to 3 show a quantitative comparison of the pressure loss calculation in nPro and data from the pipe manufacturer ENERPIPE. The ENERPIPE data are based on a company brochure with data for a CaldoPEX pipe at 80 °C supply temperature and 60 °C return temperature (brochure: “ENERPIPE - Nahwärmetechnik die ankommt.”, 01/2021, pp. 34-35). Tables 4 to 7 present a quantitative comparison between the pressure loss calculations of nPro and the results of the online tool druckverlust.de. Tables 4 and 5 specifically validate the results for laminar flows and Tables 6 and 7 for turbulent flows.

Table 1: Comparison of pressure gradients calculated with nPro and the values given by ENERPIPE for a volume flow of 12.5 l/s (temperature difference: 20 K, thermal power: 1022.9 kW) and a surface roughness of 0.007 mm.

Inner diameter	nPro	ENERPIPE	Deviation
90 mm	300 Pa/m	297.1 Pa/m	1.0 %
102.2 mm	161 Pa/m	158.8 Pa/m	1.4 %
114.6 mm	92 Pa/m	90.6 Pa/m	1.5 %

Table 2: Comparison of pressure gradients calculated with nPro and the values given by ENERPIPE for a volume flow of 20 l/s (temperature difference: 20 K, thermal power: 1636.6 kW) and a surface roughness of 0.007 mm.

Inner diameter	nPro	ENERPIPE	Deviation
114.6 mm	219 Pa/m	217.3 Pa/m	0.8 %
130.8 mm	115 Pa/m	113.3 Pa/m	1.5 %

Table 3: Comparison of pressure gradients calculated with nPro and the values given by ENERPIPE for a volume flow of 1 l/s (temperature difference: 20 K, thermal power: 81.8 kW) and a surface roughness of 0.007 mm.

Inner diameter	nPro	ENERPIPE	Deviation
32.6 mm	411 Pa/m	403.6 Pa/m	1.8 %
40.8 mm	139 Pa/m	135.1 Pa/m	2.9 %
51.4 mm	46 Pa/m	44.1 Pa/m	4.3 %

Table 4: Comparison of pressure gradients for a laminar flow calculated with nPro and the results from the tool druckverlust.de for a surface roughness of 0.15 mm (Temperature: 70°C, Temperature difference: 20 K) .

Inner diameter	Reynolds number	nPro	druckverlust.de	Abweichung
21.7 mm	1700	1.18 Pa/m	1.25 Pa/m	5.4 %
27.3 mm	1300	0.452 Pa/m	0.447 Pa/m	1.2 %
50 mm	1300	0.074 Pa/m	0.075 Pa/m	0.9 %
100 mm	2000	0.014 Pa/m	0.013 Pa/m	5.7 %
170 mm	300	0.00043 Pa/m	0.000425 Pa/m	1.1 %

Table 5: Comparison of pressure gradients for a laminar flow calculated with nPro and the results from the tool druckverlust.de for an inner diameter of 40 mm (Temperature: 70 °C, Temperature difference: 20 K) and a surface roughness of 0.15 mm.

Flow velocity	Power	nPro	druckverlust.de	Deviation
0.0047 m/s	0.49 kW	0.044 Pa/m	0.044 Pa/m	0.0 %
0.0083 m/s	0.85 kW	0.077 Pa/m	0.077 Pa/m	0.0 %
0.014 m/s	1.47 kW	0.133 Pa/m	0.133 Pa/m	0.0 %
0.02 m/s	2.08 kW	0.188 Pa/m	0.188 Pa/m	0.0 %
0.023 m/s	2.45 kW	0.221 Pa/m	0.211 Pa/m	0.0 %
0.027 m/s	2.8 kW	0.25 Pa/m	0.255 Pa/m	1.9 %

Table 6: Comparison of pressure gradients for a turbulent flow calculated with nPro and the results from the tool druckverlust.de for an inner diameter of 50 mm (Temperature: 70°C, Temperature difference: 20 K) and a surface roughness of 0.15 mm.

Flow velocity	Power	nPro	druckverlust.de	Deviation
0.1 m/s	16.1 kW	3.52 Pa/m	3.4 Pa/m	3.5 %
0.25 m/s	40.4 kW	19 Pa/m	18.7 Pa/m	0.7 %
0.5 m/s	80.6 kW	70.2 Pa/m	70 Pa/m	0.3 %
1 m/s	161.1 kW	269.3 Pa/m	268 Pa/m	0.5 %
1.5 m/s	241.6 kW	596.9 Pa/m	595 Pa/m	0.3 %
2 m/s	322.1 kW	1052.9 Pa/m	1049.3 Pa/m	0.3 %

Table 7: Comparison of pressure gradients for a turbulent flow calculated with nPro and the results from the tool druckverlust.de for an inner diameter of 100 mm (Temperature: 70°C, Temperature difference: 20 K) and a surface roughness of 0.15 mm.

Flow velocity	Power	nPro	druckverlust.de	Deviation
0.1 m/s	64.5 kW	1.44 Pa/m	1.4 Pa/m	3.1 %
0.25 m/s	161.1 kW	7.8 Pa/m	7.7 Pa/m	1.2 %
0.5 m/s	322.1 kW	29.1 Pa/m	28.9 Pa/m	0.8 %
1 m/s	645.1 kW	111.8 Pa/m	111.6 Pa/m	0.2 %
1.5 m/s	969.7 kW	247.8 Pa/m	248.6 Pa/m	0.3 %
2 m/s	1290.2 kW	437.18 Pa/m	436.8 Pa/m	0.1 %