{"id":4396,"date":"2025-12-09T10:49:28","date_gmt":"2025-12-09T09:49:28","guid":{"rendered":"https:\/\/ghetool.eu\/?post_type=knowledgebase&#038;p=4396"},"modified":"2026-04-27T16:46:56","modified_gmt":"2026-04-27T14:46:56","slug":"exercice-sur-la-perte-de-charge","status":"publish","type":"knowledgebase","link":"https:\/\/ghetool.eu\/fr_fr\/knowledgebase\/exercise-on-pressure-drop\/","title":{"rendered":"Exercice sur le calcul des pertes de charge"},"content":{"rendered":"<p>The pressure drop and the thermal behaviour of borefields are the two aspects that are important for every design. In this exercise, we will take a closer look at the pressure drop, how it changes with different design options, and how it relates to our newest method.<\/p>\n<p><iframe title=\"Exercise on the pressure drop calculation\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/Jt7_r-YbJXk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<h2>The exercise<\/h2>\n<p data-start=\"83\" data-end=\"385\">To stay in the mood for the approaching holiday season, we will take a look at a fictitious old bookstore in the city of Bremen (Germany). The whole corner block is being renovated and will be heated (and to a lesser extent cooled) with a geothermal borefield that can be drilled under a nearby square.<\/p>\n<p data-start=\"387\" data-end=\"893\" data-is-last-node=\"\" data-is-only-node=\"\">The goal of this exercise is to learn how the thermal design of a borefield also influences the hydraulic aspects, namely the choice between a single or double U tube, and whether the boreholes are connected in parallel, Tichelmann (reverse return), or in series. In addition, we will also learn how to calculate (or estimate) the flow rate through the entire borefield, as well as how the latest method to calculate both the required borehole size and depth (see our article <a href=\"https:\/\/ghetool.eu\/knowledgebase\/calculate-required-borefield-size\/\">here<\/a>) can speed up our design.<\/p>\n<figure id=\"attachment_4398\" aria-describedby=\"caption-attachment-4398\" style=\"width: 1063px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-4398 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore.jpg\" alt=\"Image of the example building for the pressure drop calculation exercise.\" width=\"1063\" height=\"1865\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore.jpg 1063w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore-171x300.jpg 171w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore-584x1024.jpg 584w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore-768x1347.jpg 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore-875x1536.jpg 875w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Bookstore-7x12.jpg 7w\" sizes=\"(max-width: 1063px) 100vw, 1063px\" \/><figcaption id=\"caption-attachment-4398\" class=\"wp-caption-text\">Image of the example building for the pressure drop calculation exercise.<\/figcaption><\/figure>\n<blockquote><p><span style=\"color: #339966;\"><strong>!Hint<br \/>\n<\/strong>To get the most out of this exercise, we strongly recommend attempting the design questions below before reading the provided solution. Borefield design is far from straightforward, and the best way to master its complexities is through hands-on experience.<\/span><\/p><\/blockquote>\n<h3>Input parameters<\/h3>\n<p><strong>General input parameters<\/strong><\/p>\n<ul>\n<li>Minimum average fluid temperature threshold: -2\u00b0C<\/li>\n<li>Maximum average fluid temperature threshold: 17\u00b0C (passive cooling)<\/li>\n<li>Simulation period: 50 years<\/li>\n<li>First month of the simulation: January<\/li>\n<\/ul>\n<p><strong>Ground input parameters<\/strong><\/p>\n<ul>\n<li>Ground thermal conductivity: 1.6 W\/(mK)<\/li>\n<li>Volumetric heat capacity: 2.4 MJ\/(m\u00b3K)<\/li>\n<li>Surface temperature: 10\u00b0C<\/li>\n<li>Geothermal heat flux: 0.8 W\/m\u00b2<\/li>\n<\/ul>\n<p><strong>Borehole resistance input parameters<\/strong><\/p>\n<p>The parameters for the pipe are:<\/p>\n<ul>\n<li>Double DN32 PN16 pipe (i.e. a wall thickness of 3mm and an outer diameter of 32mm)<\/li>\n<li>Borehole diameter: 140 mm<\/li>\n<li>Distance from pipe to borehole centre: 35 mm<\/li>\n<li>Grout: 1.8 W\/(mK)<\/li>\n<\/ul>\n<p>The fluid is 25 v\/v% MPG with a temperature difference of 3\u00b0C across the borefield.<\/p>\n<p><strong>Thermal load input parameters<\/strong><\/p>\n<ul>\n<li>Peak heating demand: 37 kW<\/li>\n<li>Yearly heating demand: 67 MWh<\/li>\n<li>Peak cooling demand: 4 kW<\/li>\n<li>Yearly cooling demand: 2.9 MWh<\/li>\n<li>SCOP: 5<\/li>\n<li>SEER: 20<\/li>\n<li>Peak duration heating\/cooling: 8 hours<\/li>\n<\/ul>\n<p><strong>Borefield configuration<\/strong><\/p>\n<p>As a borefield configuration, a regular grid of 3 x 4 boreholes with a borehole depth of 120 m is selected. The buried depth is 0.7 m and the borehole spacing, as visible in the figure below, 6 m in both length and width direction.<\/p>\n<p><strong>Hydraulic configuration<\/strong><\/p>\n<p>The image below shows the position of the borehole relative to the corner building. The longest path from one borehole to the manifold is shown in light blue. This horizontal distance is 30 m.<\/p>\n<blockquote><p><span style=\"color: #3366ff;\"><strong>!Note<\/strong><\/span><br \/>\n<span style=\"color: #3366ff;\">As mentioned in <a style=\"text-decoration: underline;\" href=\"https:\/\/ghetool.eu\/knowledgebase\/pressure-drop-and-pump-energy-in-ghetool\/\">our article<\/a> on the pressure drop calculations, we only need the worst-case horizontal connection, that is the longest one, to calculate the pressure drop of the entire borefield.<\/span><\/p><\/blockquote>\n<figure id=\"attachment_4397\" aria-describedby=\"caption-attachment-4397\" style=\"width: 1983px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-4397 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration.png\" alt=\"Configuration of the borefield with the longest path of the horizontal connection from the borehole to the collector.\" width=\"1983\" height=\"1410\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration.png 1983w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration-300x213.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration-1024x728.png 1024w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration-768x546.png 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration-1536x1092.png 1536w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Configuration-18x12.png 18w\" sizes=\"(max-width: 1983px) 100vw, 1983px\" \/><figcaption id=\"caption-attachment-4397\" class=\"wp-caption-text\">Configuration of the borefield with the longest path of the horizontal connection from the borehole to the collector.<\/figcaption><\/figure>\n<h3>Design questions<\/h3>\n<p>For this exercise, you are invited to answer the following design questions while tracking the total borehole length for each step. This will help you assess the cost and performance implications of various design changes.<\/p>\n<blockquote><p><span style=\"color: #339966;\"><strong>!Hint<br \/>\n<\/strong>To keep your work well-organised, it is recommended to use a separate scenario for each design question.<\/span><\/p><\/blockquote>\n<ol>\n<li>Calculate the temperature profile and pressure drop with all the boreholes in parallel.<\/li>\n<li>Calculate the temperature profile and pressure drop with the boreholes connected in pairs of two in Tichelmann. What happens to the pressure drop in the borehole and in the horizontal connections?<\/li>\n<li>Calculate the temperature profile and pressure drop with the boreholes connected in pairs of two in series. What happens to the pressure drop in the borehole and in the horizontal connections?<\/li>\n<li>Let us keep the series connection and use a single DN40 instead of a double DN32. What is the resulting temperature and pressure drop?<\/li>\n<li>Use the new method to automatically calculate the required borefield size and depth (with the default settings) and use a series factor of 1. What is the proposed configuration? Can we explain this?<\/li>\n<li>Let us now do the same, but set the flow rate per borehole instead of for the entire borefield. Use the same flow rate you calculated, but divide it by the initial 12 boreholes. How does the optimal design change?<\/li>\n<\/ol>\n<h2>Calculate the flow rate<\/h2>\n<p>Before we can get started with the exercise, the flow rate through the entire borefield must be calculated. One way to do this is to look at the technical datasheet of the heat pump and search for the pump characteristics (see <a style=\"text-decoration: underline;\" href=\"https:\/\/ghetool.eu\/knowledgebase\/pressure-drop\/\">our article<\/a> on this topic). However, when the heat pump is not yet selected, this is not an option. Another way is to calculate this based on the peak power of the heat pump, the efficiency, and the required difference between the borefield inlet and outlet temperature, which typically is between 3\u20135 \u00b0C.<\/p>\n<p>Mass flow rate, temperature, and power are all connected via the following formula: $$\\dot{Q}=\\dot{m} \\cdot C_p \\cdot \\Delta T$$<\/p>\n<p>where $\\dot{Q}$ is the power (in kW), $\\dot{m}$ is the mass flow rate through the system (in kg\/s), $\\Delta T$ is the temperature difference between inlet and outlet (in \u00b0C), and $C_p$ is the specific heat capacity of the heat transfer fluid (in kJ\/(kgK)). This last parameter depends on the type of antifreeze used, the fluid temperature, etc, but is generally around 4 kJ\/(kgK). Therefore, the flow rate can be calculated as: $$\\dot{m}=\\frac{\\dot{Q}}{4\\cdot \\Delta T}$$<\/p>\n<blockquote><p><span style=\"color: #ff9900;\"><strong>!Caution<\/strong><\/span><br \/>\n<span style=\"color: #ff9900;\">Please note that the power in the formula above is the extraction or injection power of the heat pump, not the heating or cooling capacity. Therefore, it is important to take the efficiency into account to translate the building power to a geothermal one.<\/span><\/p>\n<p><span style=\"color: #339966;\"><strong>!Stay tuned<\/strong><\/span><br \/>\n<span style=\"color: #339966;\">This rule of thumb can be used to estimate the flow rate through the system, but of course, since the heat pump can modulate and the specific heat capacity fluctuates as well, this flow rate is not constant. Therefore, next month, we will release a feature in GHEtool Cloud where you can specify the required $\\Delta T$ so the software can calculate the corresponding flow rate for you.<\/span><\/p><\/blockquote>\n<h2>Solution<\/h2>\n<p>Below you\u2019ll find the answers to the design questions outlined earlier. It is important to emphasise that there is no single correct answer. The value of this exercise lies in understanding the reasoning behind each decision rather than strictly agreeing with every assumption.<\/p>\n<p>Each geothermal project is unique, and the choices you make\u2014regarding parameters, configurations, and thresholds\u2014depend heavily on project-specific constraints, design priorities, and practical considerations. Use these answers as a guide, but don\u2019t hesitate to challenge the assumptions and explore alternatives.<\/p>\n<h3>Question 1<\/h3>\n<article class=\"text-token-text-primary w-full focus:outline-none [--shadow-height:45px] has-data-writing-block:pointer-events-none has-data-writing-block:-mt-(--shadow-height) has-data-writing-block:pt-(--shadow-height) [&amp;:has([data-writing-block])&gt;*]:pointer-events-auto scroll-mt-[calc(var(--header-height)+min(200px,max(70px,20svh)))]\" dir=\"auto\" tabindex=\"-1\" data-turn-id=\"request-WEB:c693274c-7838-4a93-9cd1-885f8527bc22-8\" data-testid=\"conversation-turn-16\" data-scroll-anchor=\"true\" data-turn=\"assistant\">\n<div class=\"text-base my-auto mx-auto pb-10 [--thread-content-margin:--spacing(4)] @w-sm\/main:[--thread-content-margin:--spacing(6)] @w-lg\/main:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:40rem] @w-lg\/main:[--thread-content-max-width:48rem] mx-auto max-w-(--thread-content-max-width) flex-1 group\/turn-messages focus-visible:outline-hidden relative flex w-full min-w-0 flex-col agent-turn\" tabindex=\"-1\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-1\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"c2148f20-7f31-4396-94cd-445ecb1507ee\" data-message-model-slug=\"gpt-5-1\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[1px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light markdown-new-styling\">\n<p data-start=\"84\" data-end=\"492\" data-is-last-node=\"\" data-is-only-node=\"\">With the efficiency of the heat pump being 5, we know that 4\/5 (i.e. 80%) of its peak power is actually extraction power. When we use the formula above to calculate the flow rate, we end up with a flow rate of around 2.5 kg\/s for the entire borefield. This gives us a temperature profile like the one below, where the minimum average fluid temperature is, with -0.29 \u00b0C, slightly below our threshold of 0 \u00b0C.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<figure id=\"attachment_4400\" aria-describedby=\"caption-attachment-4400\" style=\"width: 1420px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-4400 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temp-scenario-1.png\" alt=\"Temperature profile of the first scenario where every borehole is connected in parallel.\" width=\"1420\" height=\"500\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temp-scenario-1.png 1420w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temp-scenario-1-300x106.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temp-scenario-1-1024x361.png 1024w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temp-scenario-1-768x270.png 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temp-scenario-1-18x6.png 18w\" sizes=\"(max-width: 1420px) 100vw, 1420px\" \/><figcaption id=\"caption-attachment-4400\" class=\"wp-caption-text\">Temperature profile of the first scenario where every borehole is connected in parallel.<\/figcaption><\/figure>\n<article class=\"text-token-text-primary w-full focus:outline-none [--shadow-height:45px] has-data-writing-block:pointer-events-none has-data-writing-block:-mt-(--shadow-height) has-data-writing-block:pt-(--shadow-height) [&amp;:has([data-writing-block])&gt;*]:pointer-events-auto scroll-mt-[calc(var(--header-height)+min(200px,max(70px,20svh)))]\" dir=\"auto\" tabindex=\"-1\" data-turn-id=\"request-WEB:c693274c-7838-4a93-9cd1-885f8527bc22-9\" data-testid=\"conversation-turn-18\" data-scroll-anchor=\"true\" data-turn=\"assistant\">\n<div class=\"text-base my-auto mx-auto pb-10 [--thread-content-margin:--spacing(4)] @w-sm\/main:[--thread-content-margin:--spacing(6)] @w-lg\/main:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:40rem] @w-lg\/main:[--thread-content-max-width:48rem] mx-auto max-w-(--thread-content-max-width) flex-1 group\/turn-messages focus-visible:outline-hidden relative flex w-full min-w-0 flex-col agent-turn\" tabindex=\"-1\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-1\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"9d431df5-70d4-4f1a-8f03-0179167a754d\" data-message-model-slug=\"gpt-5-1\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[1px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light markdown-new-styling\">\n<p data-start=\"74\" data-end=\"380\" data-is-last-node=\"\" data-is-only-node=\"\">The flow is very laminar (Re = 839 in extraction), and this gives us a pressure drop across the borehole of 13.11 kPa and 2.7 kPa across the horizontal connection. In the graph below, you can clearly see a jump at around 4 l\/s flow rate. This is the point where our horizontal connections become turbulent.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<figure id=\"attachment_4399\" aria-describedby=\"caption-attachment-4399\" style=\"width: 585px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4399 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-1.png\" alt=\"The pressure drop curve of the first scenario where every borehole is connected in parallel.\" width=\"585\" height=\"500\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-1.png 585w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-1-300x256.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-1-14x12.png 14w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><figcaption id=\"caption-attachment-4399\" class=\"wp-caption-text\">The pressure drop curve of the first scenario where every borehole is connected in parallel.<\/figcaption><\/figure>\n<h3>Question 2<\/h3>\n<p>As a second option, we will put the boreholes in groups of two in Tichelmann (see <a style=\"text-decoration: underline;\" href=\"https:\/\/ghetool.eu\/knowledgebase\/advanced-pressure-drop-calculations\/\">our article<\/a> on this topic to learn more). This minimises the cost of the total system by halving the number of required horizontal connections and using a smaller manifold with now only 6 instead of 12 connections. The pressure drop in the borehole, as well as the thermal behaviour of the system itself, is still the same, but the pressure drop in the horizontal connections has increased to 10.19 kPa due to the higher flow rate.<\/p>\n<p data-start=\"601\" data-end=\"763\" data-is-last-node=\"\" data-is-only-node=\"\">As you can see in the graph below, the jump is now below our designed flow rate, meaning the horizontal pipes are turbulent. The entire pressure drop is 23.3 kPa.<\/p>\n<figure id=\"attachment_4401\" aria-describedby=\"caption-attachment-4401\" style=\"width: 585px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4401 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-2.png\" alt=\"The pressure drop curve of the first scenario where every the boreholes are connected in groups of 2 in Tichelmann.\" width=\"585\" height=\"500\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-2.png 585w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-2-300x256.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-2-14x12.png 14w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><figcaption id=\"caption-attachment-4401\" class=\"wp-caption-text\">The pressure drop curve of the second scenario where every the boreholes are connected in groups of 2 in Tichelmann.<\/figcaption><\/figure>\n<h3>Question 3<\/h3>\n<p data-start=\"88\" data-end=\"588\">Because we are still in a laminar flow regime, our borehole resistance for the first two cases was only 0.1535 mK\/W, which is not that great. Therefore, in this scenario, instead of connecting the boreholes in Tichelmann, we will connect them in series to double the flow rate through each borehole. The pressure drop in the horizontal connections is the same as in the previous case, but the pressure drop across one borehole is now 25.85 kPa and the flow is still laminar (Re = 1703 in extraction).<\/p>\n<p data-start=\"590\" data-end=\"754\">The borehole thermal resistance is therefore only slightly better (0.1388 mK\/W), giving us a minimum average fluid temperature of 0.01 \u00b0C, just above the threshold.<\/p>\n<p data-start=\"756\" data-end=\"1156\" data-is-last-node=\"\" data-is-only-node=\"\">It is important to note that, since the boreholes are now connected in series, the entire pressure drop across the borefield is equal to two times the pressure drop of one borehole plus the horizontal connection. This gives a total pressure drop of 61.85 kPa. In the graph below, a second jump is now also visible where the double DN32 becomes turbulent. This is, however, above our design flow rate.<\/p>\n<figure id=\"attachment_4403\" aria-describedby=\"caption-attachment-4403\" style=\"width: 585px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4403 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-3.png\" alt=\"The pressure drop curve of the first scenario where every the boreholes are connected in groups of 2 in series.\" width=\"585\" height=\"500\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-3.png 585w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-3-300x256.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-3-14x12.png 14w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><figcaption id=\"caption-attachment-4403\" class=\"wp-caption-text\">The pressure drop curve of the third scenario where every the boreholes are connected in groups of 2 in series.<\/figcaption><\/figure>\n<h3>Question 4<\/h3>\n<article class=\"text-token-text-primary w-full focus:outline-none [--shadow-height:45px] has-data-writing-block:pointer-events-none has-data-writing-block:-mt-(--shadow-height) has-data-writing-block:pt-(--shadow-height) [&amp;:has([data-writing-block])&gt;*]:pointer-events-auto scroll-mt-[calc(var(--header-height)+min(200px,max(70px,20svh)))]\" dir=\"auto\" tabindex=\"-1\" data-turn-id=\"request-WEB:c693274c-7838-4a93-9cd1-885f8527bc22-12\" data-testid=\"conversation-turn-24\" data-scroll-anchor=\"true\" data-turn=\"assistant\">\n<div class=\"text-base my-auto mx-auto pb-10 [--thread-content-margin:--spacing(4)] @w-sm\/main:[--thread-content-margin:--spacing(6)] @w-lg\/main:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:40rem] @w-lg\/main:[--thread-content-max-width:48rem] mx-auto max-w-(--thread-content-max-width) flex-1 group\/turn-messages focus-visible:outline-hidden relative flex w-full min-w-0 flex-col agent-turn\" tabindex=\"-1\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-1\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"f125916c-4abe-4cb9-bad9-c7c4d4de9879\" data-message-model-slug=\"gpt-5-1\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[1px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light markdown-new-styling\">\n<p data-start=\"84\" data-end=\"413\" data-is-last-node=\"\" data-is-only-node=\"\">As a second attempt to bring the borehole into a turbulent flow regime, we go for a single DN40 instead of a double DN32, whilst still being in groups of 2 in series. This gives us a transitional flow regime (Re = 2742 in extraction) and a borehole resistance of 0.1290 mK\/W. The minimum average fluid temperature is now 0.21 \u00b0C.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<figure id=\"attachment_4404\" aria-describedby=\"caption-attachment-4404\" style=\"width: 1420px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4404 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temperature-profile-scenario-4.png\" alt=\"Temperature profile of the fourth scenario with single DN40 probes connected per two in series.\" width=\"1420\" height=\"500\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temperature-profile-scenario-4.png 1420w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temperature-profile-scenario-4-300x106.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temperature-profile-scenario-4-1024x361.png 1024w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temperature-profile-scenario-4-768x270.png 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Temperature-profile-scenario-4-18x6.png 18w\" sizes=\"(max-width: 1420px) 100vw, 1420px\" \/><figcaption id=\"caption-attachment-4404\" class=\"wp-caption-text\">Temperature profile of the fourth scenario with single DN40 probes connected per two in series.<\/figcaption><\/figure>\n<p data-start=\"87\" data-end=\"394\">The pressure drop for a single borehole, due to the turbulence, increased to 39.75 kPa, bringing the entire pressure drop to 89.61 kPa. In the graph below, you can see that there is now only one jump in the pressure drop, since both the horizontal and vertical connections are DN40s with the same flow rate.<\/p>\n<blockquote><p><span style=\"color: #3366ff;\"><strong>!Note<\/strong><\/span><br \/>\n<span style=\"color: #3366ff;\">Although the mass flow rate has not changed, there is a slight difference in the pressure drop for the horizontal connections, now 10.11 kPa instead of 10.14 kPa before. Due to a different thermal behaviour, the fluid temperature is ever so slightly higher, giving a different fluid density and hence a different volume flow rate in l\/s for the same and constant mass flow rate.<\/span><\/p><\/blockquote>\n<figure id=\"attachment_4405\" aria-describedby=\"caption-attachment-4405\" style=\"width: 585px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4405 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-4.png\" alt=\"Pressure drop of the fourth scenario with single DN40 probes connected per two in series.\" width=\"585\" height=\"500\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-4.png 585w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-4-300x256.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/12\/Pressure-drop-scenario-4-14x12.png 14w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><figcaption id=\"caption-attachment-4405\" class=\"wp-caption-text\">Pressure drop of the fourth scenario with single DN40 probes connected per two in series.<\/figcaption><\/figure>\n<h3>Question 5<\/h3>\n<p data-start=\"142\" data-end=\"556\">In the scenarios above, we played around manually to find a good solution. The other alternative is to let GHEtool Cloud optimise this for you. When we set the series factor back to 1 and use the \u201ccalculate required size and depth\u201d aim (with the default settings), the algorithm finds a solution with just 6 boreholes of 183.52 m deep, giving us a total borehole length of 1097 m instead of the 1432 m from before.<\/p>\n<p data-start=\"558\" data-end=\"596\">The reasoning behind this solution is:<\/p>\n<ul>\n<li data-start=\"598\" data-end=\"908\">Drilling deeper gives a warmer ground temperature, which is beneficial in this extraction dominated and limited case (see <a style=\"text-decoration: underline;\">our article<\/a> on borefield quadrants).<\/li>\n<li data-start=\"598\" data-end=\"908\">Fewer boreholes mean having a higher flow rate per borehole, and this optimal solution also has a transitional flow regime (Re = 2716 in extraction).<\/li>\n<\/ul>\n<blockquote><p><span style=\"color: #ff9900;\"><strong>!Caution<\/strong><\/span><br \/>\n<span style=\"color: #ff9900;\">Be aware that the horizontal length for the pressure drop calculation is not automatically updated when using this method.<\/span><\/p><\/blockquote>\n<h3>Question 6<\/h3>\n<p data-start=\"1066\" data-end=\"1587\">As a last variation, the same simulation is done as above, but now assuming a flow rate per borehole of 0.205 kg\/s, which gives the same flow rate as before for our 12 boreholes. If we now run the simulation, we need 7 boreholes of around 193.8 m, which is significantly more than before. Since the flow rate is now fixed per borehole, the algorithm cannot optimise towards a turbulent regime with better heat transfer. Besides that, our total flow rate is now 1.435 kg\/s, which is lower than the design flow rate we had.<\/p>\n<p data-start=\"1589\" data-end=\"1725\">It should be clear that when you use the \u201ccalculate required size and depth\u201d aim, you should use the flow rate for the entire borefield.<\/p>\n<h2>Conclusion<\/h2>\n<article class=\"text-token-text-primary w-full focus:outline-none [--shadow-height:45px] has-data-writing-block:pointer-events-none has-data-writing-block:-mt-(--shadow-height) has-data-writing-block:pt-(--shadow-height) [&amp;:has([data-writing-block])&gt;*]:pointer-events-auto scroll-mt-[calc(var(--header-height)+min(200px,max(70px,20svh)))]\" dir=\"auto\" tabindex=\"-1\" data-turn-id=\"request-WEB:c693274c-7838-4a93-9cd1-885f8527bc22-14\" data-testid=\"conversation-turn-28\" data-scroll-anchor=\"true\" data-turn=\"assistant\">\n<div class=\"text-base my-auto mx-auto pb-10 [--thread-content-margin:--spacing(4)] @w-sm\/main:[--thread-content-margin:--spacing(6)] @w-lg\/main:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:40rem] @w-lg\/main:[--thread-content-max-width:48rem] mx-auto max-w-(--thread-content-max-width) flex-1 group\/turn-messages focus-visible:outline-hidden relative flex w-full min-w-0 flex-col agent-turn\" tabindex=\"-1\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-1\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"6aa70772-4b6a-4717-8dca-716d375ba3e5\" data-message-model-slug=\"gpt-5-1\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[1px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light markdown-new-styling\">\n<p data-start=\"1748\" data-end=\"2163\" data-is-last-node=\"\" data-is-only-node=\"\">In this exercise, a closer look was taken at the pressure drop simulation for parallel, Tichelmann, and series connections. In addition, the difference between a double DN32 and a single DN40 was investigated. It was shown that when you use the method to calculate the required borefield size and depth, it is better to work with the flow rate per borefield instead of per borehole to avoid mistakes and oversizing.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<h2 id=\"reference\">References<\/h2>\n<ul>\n<li>Watch our video explanation over on our YouTube page by clicking <span style=\"text-decoration: underline;\"><a href=\"https:\/\/youtu.be\/Jt7_r-YbJXk\" target=\"_blank\" rel=\"noopener\">here<\/a><\/span>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>La perte de charge et le comportement thermique des champs de forage sont deux aspects importants pour chaque conception. Dans cet exercice, nous examinerons de plus pr\u00e8s la perte de charge, la mani\u00e8re dont elle \u00e9volue en fonction des diff\u00e9rentes options de conception et la mani\u00e8re dont elle est li\u00e9e \u00e0 notre m\u00e9thode la plus r\u00e9cente.<\/p>","protected":false},"template":"","pdf-article":[110],"authors":[39],"knowledgebase-category":[82],"class_list":["post-4396","knowledgebase","type-knowledgebase","status-publish","hentry","pdf-article-exercise-pressure-drop","authors-wouter-peere","knowledgebase-category-exercise"],"_links":{"self":[{"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/knowledgebase\/4396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/types\/knowledgebase"}],"wp:attachment":[{"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/media?parent=4396"}],"wp:term":[{"taxonomy":"pdf-article","embeddable":true,"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/pdf-article?post=4396"},{"taxonomy":"authors","embeddable":true,"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/authors?post=4396"},{"taxonomy":"knowledgebase-category","embeddable":true,"href":"https:\/\/ghetool.eu\/fr_fr\/wp-json\/wp\/v2\/knowledgebase-category?post=4396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}