Borefields are often designed by considering only the thermal aspects, but the hydraulic counterpart is just as important for both system performance and feasibility. In this chapter, the concept of pressure drop, which is central to hydraulic design, will be explained.
What is pressure drop?
The pressure drop is a fluid dynamic concept defined as the difference in pressure between point A and B due to friction, and this friction element is crucial. This friction can occur between the fluid and the pipe walls, the valves, pumps, etc., but also within the fluid itself, between different fluid ‘droplets’. The pressure drop can therefore be seen as the effort required to move the fluid through the system. Although the pressure drop can be a complicated parameter to calculate, the following parameters play a role:
- Pipe length, diameter, and viscosity. If you have a longer pipe or one with a smaller diameter, you will have a harder time pushing the fluid around. The same applies to viscosity: if you were to fill your borefield with honey, which has a very high viscosity, you can imagine the amount of effort required to move it through the system.
- Routing. A borefield where the horizontal connections between boreholes are straight and parallel will allow fluid to flow more easily than one where boreholes are connected with lots of bends or right-angled connections.
Both aspects contribute to the calculation of the pressure drop and are respectively called friction losses (major losses) and local losses (minor losses). Both are explained below, in reverse order, for ease of understanding.
Local losses
Local losses (also called minor losses) account for pressure drop contributions that can be pinpointed to specific components in the hydraulic design. These include bends, interconnections, valves, etc. The table below shows a few examples of different local losses, which are defined by a factor $K$.
There is no definitive answer to the exact local loss factor for a specific component. The values above serve as a general guideline, but other sources are provided in the references. When you know exactly which products will be used, you can ask your supplier for the specific values, as they typically have this information.
As seen in the table, a smooth bend (especially when flanged) has a lower loss factor than a right-angled bend, which aligns with expectations. Similarly, 45° bends have lower loss factors than 90° bends.
Given the local pressure drop factors above, the following formula can be used to convert them into a general pressure drop:$$\Delta P=\left(\sum K\right)\cdot \frac{\rho v^2}{2}$$where $\Delta P$ is the pressure drop in (Pa), $\rho$ is the fluid density in (kg/m³) and $v$ is the fluid velocity in the pipe in (m/s).
This means that the total contribution of the local pressure drops to the overall pressure drop, is simply determined by summing all different K-values following a certain hydraulic path and multiplying it by $\rho v^2/2$.
Friction losses
Friction losses (also called major losses) are pressure drops that cannot be attributed to specific components but instead occur throughout the entire system. These are calculated using the well-known Darcy-Weisbach formula:
$$\Delta P = f \cdot \frac{L}{D}\cdot \frac{\rho v^2}{2}$$where $\Delta P$ is again the pressure drop in (Pa), $f$ is the dimensionless Darcy-Weisbach friction factor, $L$ is the length of the pipe in (m), $D$ is the diameter of the pipe in (m), and $\rho$ and $v$ are respectively the fluid density in (kg/m³) and the fluid velocity in (m/s).
This aligns with intuition, as a longer pipe results in higher pressure drops. The only new factor here is the Darcy-Weisbach friction factor, which can be found using the Moody diagram.
Moody diagram
The Moody diagram is a well-known graph in fluid dynamics that can be used to determine the Darcy-Weisbach friction factor for different Reynolds numbers and is presented on a log-log scale. This means that lines of equal increments (from 1 to 2 to 3, etc.) are not equally spaced.
In the Moody diagram, three different flow regimes are shown: the laminar regime on the left, the transitional regime in the middle, and the turbulent regime on the right. (If you do not recall the different flow regimes, please revisit Part 2.2.)
Laminar region (Re<2300)
In the laminar region, the friction factor can be defined analytically as $64/Re$. This means that, as long as the flow remains in the laminar regime, increasing the Reynolds number (for example by increasing the flow rate or decreasing the viscosity) will result in a lower friction factor and, consequently, potentially a lower pressure drop.
Turbulent region (Re>4000)
In contrast to the laminar regime, there is no unique friction factor for the turbulent regime, since it depends on the relative pipe roughness (i.e. the pipe roughness divided by the pipe diameter). In the case of geothermal probes, this value is typically rather small (of the order of a few micrometres), approximating a smooth pipe. Multiple correlations exist, although the most widely used and standard one is the Colebrook-White equation.
The Colebrook-White equation is the standard equation used in fluid dynamics to calculate the friction factor. It is defined as $$\frac{1}{\sqrt{f}}=-2log_{10}\left(\frac{\epsilon/D}{3.7}+\frac{2.51}{Re\sqrt{f}}\right)$$where $f$ is the friction factor, $Re$ is the Reynolds number, $\epsilon$ is the pipe roughness in (m), and $D$ is the pipe diameter in (m). The main drawback of this equation is that it is implicit and requires iteration to determine $f$.
Transient region (2300<Re<4000)
As discussed in Part 2.2, the fluid does not transition directly from a laminar to a turbulent regime, but passes through a transitional phase in between, where the flow already exhibits some local turbulence but is not yet fully developed. In the case of borehole resistance and the Nusselt number, a linear interpolation has been suggested in the literature by Gnielinski (2013) to account for this transitional zone. However, for the friction factor, no such approximation exists. Therefore, the transitional zone is not considered in GHEtool when calculating the pressure drop.
There are correlations available, such as the one proposed by Churchill (1977), that account for laminar, transitional, and turbulent flow in a single equation. This equation is given by: $$f=2\left[ \left( \frac{8}{Re}\right)^{12} + \frac{1}{(A+B)^{3/2}}\right] ^{1/12}$$where$$A=\left[2.457 ln\frac{1}{(7/Re)^{0.9}+0.27 \epsilon/D}\right]^{16}$$and$$B=\left(\frac{37530}{Re}\right)^{16}$$where $f$ is the friction factor, $Re$ is the Reynolds number, $\epsilon$ is the pipe roughness in (m), and $D$ is the pipe diameter in (m).
However, according to Perry et al. (2018), a conservative approach is preferred for design purposes. Therefore, in GHEtool, the laminar region is modelled using $64/Re$, while the transitional and turbulent regions are modelled using the Colebrook-White equation.
Total pressure drop
When both local and friction losses are taken into account, the total pressure drop is given by: $$\Delta P = \left(f\cdot \frac{L}{D}+\sum{K}\right)\cdot \frac{\rho v^2}{2}$$
Below, an image is shown for a single DN40 U-probe of 100 m (so 200 m in total) with 25 v/v% MPG at 0 °C. At around 0.35 l/s, the transition from laminar to transitional or turbulent flow occurs.
Important relationships
Given the equation above, several important relationships can be derived that will be used throughout the following chapters and the rest of the course. (The full derivation is provided in the deepening insights box below.)
- $\Delta P \propto L$
This aligns with intuition: if we double the pipe length, the pressure drop across it will also double. This is, for example, important when considering parallel versus serial connections of boreholes (as will be discussed in Part 4.3). - $\Delta P \propto \dot{Q}^2$
This highlights the importance of the flow rate (and, as will be discussed in the next chapter, the use of variable flow rates). A lower flow rate will significantly reduce the pressure drop. This quadratic relationship is also clearly visible in the plot above. - $\Delta P \propto D^{-5}$
This relationship emphasises the importance of the pipe diameter of the probe, one of the key design parameters available to the designer. This relationship will be used extensively in the next part of this course.
Importance of the pressure drop
In the sections above, it was explained what pressure drop is and how it can be calculated. However, one final question remains: since geothermal borefield design is primarily concerned with keeping temperatures within certain limits, why do we need to consider the pressure drop?
Pump selection
When designing a borefield, a specific flow rate is always defined (or a variable one is used, as discussed in Part 3.3). This flow rate determines the effective borehole thermal resistance and, consequently, the overall performance of the system. However, each flow rate has an associated pressure drop, which the pump must be able to overcome. Below is an example of a pump characteristic, as typically found in technical documentation.
The red lines in the figure above represent what is known as the pump characteristic of the system at different load percentages of the circulation pump. The 100% line defines the boundary of all possible flow-pressure points that can be achieved when the circulation pump is operating at its maximum capacity.
If, for example, a system is designed for a flow rate of 0.4 l/s and has a calculated pressure drop of 33 kPa, this falls within the pump’s operating range, meaning the system can deliver this flow rate at that pressure and, therefore, everything will perform as simulated. However, if the design flow rate is 0.37 l/s but the pressure drop is 62 kPa, the pump will not be able to deliver this, and the borefield will not receive the required flow rate.
In the latter case, this means that either an additional primary circulation pump should be installed or the design should be revised so that the flow rate and pressure drop are achievable by the system.
Conclusion
This chapter introduced the concept of pressure drop and its importance for geothermal design. Both the major (friction) losses and the minor (local) losses were discussed.
Based on these insights, the next step is to explore in more detail how the pressure drop evolves over the simulation period and what its relationship is with the required pump power and pump electricity consumption.
Questions
Calculate the total local losses, i.e. the sum of all local loss factors, for the hydraulic path indicated in green below. The dotted section can be ignored.
Looking at the pressure drop curve for the DN40 probe, the first, laminar part does not show the quadratic behaviour one would expect, since $\Delta P \propto \dot{Q}$. Why?
References
- The Engineering ToolBox (2004). Pipe and Tube System Components – Minor (Dynamic) Loss Coefficients. [online] Available at: https://www.engineeringtoolbox.com/minor-loss-coefficients-pipes-d_626.html [Accessed 28-04-2026].
- Colebrook, C. F. (1939). Turbulent Flow in Pipes, with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws. Journal of the Institution of Civil Engineers. 11 (4): 133–156
- Gnielinski, V. (2013). On heat transfer in tubes. International Journal of Heat and Mass Transfer, 63, 134–140. https://doi.org/10.1016/j.ijheatmasstransfer.2013.04.015
- Perry, R.H., Green, D.W. and Southard, M.Z. (2018) Perry’s Chemical Engineers’ Handbook. 9th Edition, McGraw-Hill Education, New York, 2272. Online available here.
- Churchill, S.W. (1977). Friction Factor Equations Spans All Fluid-Flow Regimes. Chemical Engineering Journal, 84, 91-92.