Simplified math behind hydronics

By Michael Ridler 

Math doesn’t have to be difficult unless we make it so. If we struggle to understand or grasp a particular topic, it often reflects more on the instructor than the subject itself. Personally, I had a strong dislike for math during my school days. I vividly recall my math teacher asserting that I would never amount to much without his calculus class. Needless to say, I proved him wrong.

While I may not be on the same level as some of my peers, I am far from sitting on the sidelines. As Martin Luymes, vice president of government relations at the Heating, Refrigeration, and Air Conditioning Institute of Canada (HRAI), rightly points out — math would be more enjoyable if it were made more relevant to real-world applications.

Instead of focusing solely on abstract concepts like solving Pi, why not prioritize teaching practical skills such as calculating GPM and flow velocities? With that in mind, as someone heavily involved in hydronic design work, I believe it’s crucial to discuss some essential formulas and share simple “hacks” that make field calculations easier.

It’s important never to shy away from math and, more importantly, not to ignore it. Just because a designer has performed the calculations doesn’t mean they are always correct. Those of us involved in design work greatly appreciate installers who double-check and validate our designs. It’s a collaborative effort, and even though your training may be less formal, your years of experience hold as much, if not more, weight than that of the designer (speaking from personal experience in both installation and design work).

For this session on hydronic math, let’s consider a 2,000 sq. ft. house with a total load of 54,000 btu/h. Our goal is to heat this house using a boiler and a radiant floor heating system. Let’s dive into the math and demonstrate how quickly we can transform this information into a comprehensive hydronic package using nothing more than a notepad.

Turning loads into flow

We know that our home has a total load of 54,000 btu/h. The simplified formula for turning your btu/h into a flow is as follows:

That 10,000 represents a 20-degree Delta T across a radiant floor heating system, which is a common Delta T we see in residential system design. When you look at any heat loss and want to get a rough idea of your flow rates for a radiant floor heating system, the easy math is to divide the total load by 10,000. So in our case, our house load of 54,000 get divides by 10,000, which is 5.4.

Let’s look at that formula and get into the details for a second. Let’s start with the somewhat complete formula and work our way to the simplified formula.

The choice of Delta T can vary, but my personal preference is always a Delta T of 20 degrees or less. Some may opt for a 10-degree Delta T (such as applications where you have a lightweight overpour with ceramic tile to minimize temperature fluctuations), which is acceptable. However, it is crucial to avoid using a super wide Delta T in your hydronic design for a building as it can lead to uneven heating and discomfort in the space.

The value of 500 is a simplified approximation used in the sensible heat rate equation for water. It should be noted that this value is not applicable to systems that incorporate glycol, and it also changes with variations in water temperature and density. Nevertheless, for our purposes, it is more than accurate enough. Now, let’s substitute the Delta T with the previously mentioned 20 degrees and observe how our formula is transformed.

Calculating the amount of radiant tubing

When it comes to hydronic design, determining the required amount of radiant floor tubing is a crucial step. One important consideration is that the piping component is often the least expensive part of the project. By installing more tubing, you can future-proof your design as the industry transitions from boilers to heat pumps. You can even use a simple calculation to demonstrate this point by multiplying your total square footage by the value in my table for the tube spacing you have selected.

For instance, let’s take a 2,000 sq. ft. home where I want to maintain an even temperature at a low water temperature. In this case, I’ll opt for a nine-inch spacing between the tubing. Using the formula, I calculate the required tubing length as follows — 2,000 sq. ft. multiplied by 1.33, which equals 2,660 ft. of pipe.

Some installers and designers still use 12-inch spacing or even 18-inch spacing. However, with an 18-inch spacing residential tubing job, the solution often involves increasing the boiler temperature, leading to higher monthly operating costs.

Caution is essential as we approach the era of hydronic heat pumps. Adjusting water temperatures arbitrarily on equipment can result in increased maintenance or even catastrophic failures. Additionally, in other webinars, I’ve demonstrated how choosing to save $500 on tubing can add hundreds of dollars to monthly operating costs. Let’s consider our 2,000 sq. ft. home again. If we calculate it with 12-inch tubing, the result is 2,000 multiplied by 1, which equals 2,000. Assuming a cost of 50 cents per foot for PEX pipe, the project with 9-inch spacing costs $1,330, whereas the house with 12-inch spacing amounts to approximately $1,000.

Calculating manifolds

Now that we have determined our total home load to be 54,000 btu/h and the required flow rate of 5.4 GPM, let’s move on to calculating the number of manifolds needed for our system. Additionally, since we are using 9-inch spacing, we know that we will require 2,660 ft. of tubing.

Determining the required number of manifolds is a straightforward process. Assuming we are using half-inch tubing, which is commonly used in 90 per cent of residential hydronic systems, we can simply divide the total tubing length by 300. This value of 300 represents the maximum length specified by the CSA B214 standard for half-inch PEX tubing.

You might wonder why we are suggesting the maximum length of 300 right away. The reason is that the CSA B214 standard allows for a buffer of +10 per cent, meaning the actual maximum length per half-inch circuit is 330 feet. In our case, we will divide the total tubing length of 2,660 ft. by 300, resulting in approximately 8.86 manifolds. Of course, it’s not practical to have fractional manifolds, so this means we will have 8 circuits that are 300 feet long and one circuit that is shorter. Consequently, we will need a total of 9 manifolds for our system.

Calculating header pipe sizing

Now that we have determined the total load, required GPM, amount of PEX tubing, and the number of manifolds, the next step is to size the header piping that feeds the radiant manifold. In this article, we will assume that the manifold is in the mechanical room and copper piping is used for the supply.

When sizing copper piping, it is crucial to consider flow velocities. Maintaining the recommended maximum velocity is important to prevent noise and potential long-term system issues.

As per the Copper Development Association, the suggested maximum velocity for water in a copper tube system is five to eight ft. per second (FPS) for cold water systems, four to five FPS for hot water systems below 140 F, and two to three FPS for hot water systems with a temperature exceeding 140 F. Therefore, we design our heating systems around a flow rate of two to three FPS.

The minimum flow is based on two-ft. per second, while the maximum flow is based on four ft. per second. For a flow rate of 5.4 GPM, you can select either a three-quarter-inch copper pipe, which will be on the higher end of the velocity range or opt for a one-inch pipe, if you prefer to be on the lower end.

However, it’s important not to oversize the piping. Choosing excessively large pipes can introduce potential issues and unnecessary costs that your competitors, who properly size their systems, may avoid.

With all this information, we now have a comprehensive understanding to complete our design. We know that the load is 54,000 btu/h, the flow rate is 5.4 GPM, and we will be using 2,660 feet of half-inch PEX tubing with a nine-circuit manifold, all fed by three-quarter-inch piping.

Sizing the circulator

The next step in our process is sizing the circulator, which requires knowing the system pressure drop. I learned a simple trick from my close friend Dave Holdorf at Taco Comfort Solutions, which provides a reliable estimation of head loss in most cases. If you’ve completed the previous step of properly sizing your header pipes, you’ll be amazed at how accurate this basic formula can be compared to a long-form calculation.

In our scenario, where the manifold is in the mechanical room and we have a short 20-ft. of three-quarter-inch copper pipe connecting the boiler to the nine-station manifold, we can apply Holdorf’s trick. The trick involves converting the longest pipe length into a developed length and then converting it to head loss. While Holdorf likely didn’t originate this method, he taught it to me.

For our example, the 20 ft. of copper pipe is multiplied by 1.5, resulting in a calculated length of 30. The 1.5 accounts for a worst-case scenario considering the fittings in the system. Multiplying this by 0.04, which represents four-ft. of head loss per 100 feet of properly sized pipe, gives us a final head loss of 1.2 ft. for properly sized pipe. If you were to calculate the actual head loss for 5.4 GPM flowing through a three-quarter-inch copper pipe, you would get 0.7 ft. of head, but this doesn’t include all the fittings yet.

This straightforward rule of multiplying the total pipe length by 1.5 to obtain an equivalent length with fittings, and then multiplying it by 0.04 to calculate the equivalent head, is an effective method for estimating head loss. If you perform a proper calculation of the head loss, you will find this method to be accurate.

However, there is a slight flaw in the above calculation. The math we just performed is for the pipe leading to the manifold, and I did this intentionally for demonstration purposes. Usually, when we have a radiant design, we only need to calculate the piping head loss to the manifold, not the total head loss in the floor. But since we assumed there was no specific design in our case, let’s apply the method again.

We mentioned that our longest radiant floor circuit is 300 ft. long. Since we don’t have any fittings to account for (as it is impractical to use 10-foot lengths of PEX cut-offs for a floor), we can multiply the length by 0.04 and obtain 12 feet of head. For the purposes of this article, I actually designed the radiant loop using CAD software, and after all calculations, I determined that the total load was 54,375 btu/h, with a flow rate of 5.46 GPM and a total head loss of 10.1 ft., including the header piping and the radiant floor tubing.

We now know that we need a 54,000 btu/h boiler, three-quarter-inch header piping, and 2,660 ft. of half-inch PEX tubing. Additionally, we need to deliver 5.4 GPM at a head loss of 12 ft, which requires a pump capable of meeting these specifications.

The key takeaway here is not to completely ignore CAD and proper design, but rather to be open to applying effective rules of thumb to quickly assemble a material quote and estimate for a radiant floor system. These rules of thumb also come in handy when troubleshooting a system. :