The Other Heat Emitters
Although not specifically intended as a heat emitter, the piping connecting the components of a hydronic system certainly does release heat to its surroundings. Sometimes we disregard the heat output of piping, thinking it's trivial relative to that being released by the "real" heat emitters. We may even point out that if the pipe travels through heated space the heat it releases is not really "lost" heat, it's heat delivered to the space by the piping rather than the intended heat emitter.
That may be true at times, but it still compromises an important and fundamental benefit of hydronic heat -- the ability to deliver heat precisely when and where it's needed.
Heat released by the piping connecting an indirect water heater to a boiler is obviously not delivered to the intended load. Ditto for heat released by piping to heat exchangers for pools, snowmelting and other loads. The heat output of pipe passing through an unheated crawl space or attic is truly heat lost.
How Bad Is The Bleeding?Before making informed decisions about piping heat output you need to know how much heat will be released under a given set of conditions.
Chapter 22 of the 1989 ASHRAE Handbook of Fundamentals contains a table listing the heat output of bare copper tubing at different water temperatures, and when surrounded by 80-degree F air -- a typical mechanical room temperature when the equipment is operating. If you had a section of 1.5-inch copper tube filled with 180-degree F water, surrounded by 80-degree F air, you could use this table to estimate the pipe's heat output at 77.6 Btu/hr./ft.
This table gives you "snap shots" of heat loss from bare copper tubing at specific temperature differences between the inside of the tube and the surrounding air.
Suppose you need to estimate the tube's heat output at conditions not listed in the table. You could "interpolate" between the table values -- a process that, when done correctly, is about as much fun as working out your quarterly income tax payment. Or you could use the graph shown in Figure 1.
This graph is based on the data in the ASHRAE table. To use it, you first determine the temperature difference between the water in the tube and the surrounding air. Find this number on the horizontal axis and read up to the curve for the tube size you're working with. Now follow a horizontal line to the vertical axis and read the heat output.
For example, if the inside temperature of a 1-inch copper tube was 150 degrees F, and the air temperature surrounding it was 50 degrees F, the temperature difference would be 150-50, or 100 degrees F. The tube's heat output, read from the graph, is about 56 Btu/hr./ft.
The Rest Of The StoryAlthough the ASHRAE data and Figure 1 give the heat output of 1 foot of bare copper tube at certain temperatures, they don't account for what happens when the water flows through the tube.
Whenever heat is released from flowing water, its temperature drops in the downstream direction. The farther the water travels along the tube the cooler it gets, and the lower the rate of heat output from the tube's surface becomes.
If the tube is relatively short, or if the flow rate is relatively high, the temperature drop from inlet to outlet will be small, perhaps even less than one degree. In these cases, the total heat output can be estimated by looking up the heat loss per foot in Figure 1, based on the inlet temperature, and multiplying this number by the tube's length.
For example, imagine a 25-ft. length of 1.5-inch copper tube with water entering at 180 degrees F and a relatively high flow rate, say 10 gpm. Assume the pipe passes through space maintained at 65 degrees F. From Figure 1, the rate of heat output is about 92 Btu/hr./ft. The total heat output of the tube would be approximately 92 x 25, or 2,300 Btu/hr.
Although this calculation is simple, it can overestimate the tube's total heat output under certain conditions. To correct for these situations I've developed a more detailed procedure that accounts for differences in flow rate, surrounding air temperature and tube length. This procedure gives you more accurate results in situations where the tube's length in feet, divided by its flow rate in gallons per minute is greater than 20.
Chew On ThisOften, the price designers pay for better accuracy is increasingly complex mathematics and this procedure is no exception. However, that PC on your desk never complains about complex math. It can do the number crunching that gives you the most accurate results in the blink of an eye. You just have to talk to it in the right language.
To this end, I've put together a simple spreadsheet program that instantly performs the necessary math. It's shown with the associated formulas displayed in Figure 2. I've kept it very simple so it should work with almost any spreadsheet program.
Carefully copy the numbers and formulas shown in Figure 2 into your own spreadsheet.
When using it, you only need to enter the numbers shown in blue -- (cells B8 through B13). The values of C1 and C2 for the different pipe sizes are listed at the top in cells B1-B6, and C1-C6. You'll need to copy the appropriate values into cells B8 and B9 whenever you change tube size. To maintain high accuracy, be sure to copy all the digits shown.
The spreadsheet calculates the outlet temperature of the tube in cell B15. It also calculates the tube's heat output in cell B16. Both outputs are shown in red text.
Savvy spreadsheet users may want to further refine this template based on the capabilities of their own program (Excel, AppleWorks, etc.). One suggestion is to set up a routine so the appropriate numbers for C1 and C2 are automatically referenced when a given pipe size is selected.
Figure 3 shows the spreadsheet after calculating the heat output of a 1.5-inch copper tube, 100 feet long, surrounded by 80-degree F air, with water entering at 180 degrees F and 10 gpm.
Notice that the total heat output of 7,710 Btu/hr. is slightly less than what you would get by looking up the heat loss per foot in Figure 1 (about 77.6 Btu/hr./ft.) and multiplying by 100. The difference is slight for this example. However, the difference becomes much more pronounced at lower flow rates, or in situations with long tube runs. That's where this spreadsheet really shows its strength.
Precautions Are In OrderFirst, a simple spreadsheet like this doesn't protect users against "out of range" inputs. You could, for example, type in a flow rate of 1,000 gpm for a 1-inch pipe, and the program will calculate the heat output. The results would actually be pretty accurate if, through some miracle of fluid mechanics, you could figure out how to shove 1,000 gpm of water through a 1-inch copper tube. It's the same old concept you've heard many times regarding software: "Garbage in equals garbage out." Keep the input numbers realistic and you'll get realistic results.
Secondly, this routine is set up specifically for bare copper tubing carrying water. The results will not be valid for other types of tubing or fluids. They obviously will not be valid if the copper tubing is insulated.
Once this spreadsheet is on your computer you can do endless "what if" calculations without ever looking up a number in a table or graph. Use it to estimate the heat loss of piping runs through unheated or partially heated spaces. You can even use it to estimate the heat loss of copper tubing in domestic hot water distribution piping. You'll likely make some interesting discoveries about pipe heat output, in many cases finding it's not exactly "trivial."
In a future column I'll give you some modifications that allow the spreadsheet to estimate the heat output of different pipe materials, carrying different fluids, and even covered with different types of insulation. In the mean time, use this spreadsheet to get a handle on the output of the "other" heat emitters in your systems.