When “thinking mathematically,” most people think in proportions. For example, if someone is baking cookies and they want to make a double batch, they intuitively know they need to double the amount of all ingredients.

If someone was told a 100-horsepower engine, at full throttle, could make a certain car go 100 miles per hour, and was then asked how fast a 200-horsepower engine would make the same car go, he’s likely to answer 200 mph.

Unfortunately, nature doesn’t always work in proportions. NASCAR fans know it takes a lot more than 200 horsepower to push a race car around the track at 200 mph. It takes about 800 horsepower to produce that kind of speed. Most of the power goes into overcoming the aerodynamic drag of the car at those high speeds.

## A bit more complicated

Hydronics also presents its share of nonproportional relationships. One of them is how the heat output and temperature drop across a heat emitter is affected by the flow rate through it.

For example, suppose a given length of residential fin-tube was yielding an output of 5,000 Btu/hr. when operating at a flow rate of 1 gal. per min. If asked what would happen when the flow rate is doubled, while all other conditions remained the same, many people, including plenty who work with this stuff every day, would say the heat output would double.

That answer might seem intuitive but it’s far from correct.

How about if the flow rate were increased from 1 to 4 gpm? That’s a 400% increase; surely the heat output would at least double. To answer this, just look at some Institute of Boiler and Radiator Manufacturers’ output ratings from baseboard manufacturers. They’re given for a wide range of water temperatures and for flow rates of 1 gpm and 4 gpm.

You’ll find the heat output rating at a flow rate of 4 gpm is about 6% higher than the rating at 1 gpm, all other conditions being the same. The reason lies deep in the workings of natural convection and thermal radiation between the outer surface of the fin-tube element and its surroundings. Heat output is affected by the forced convection between the flowing water and the inner surface of the tube.

The theory is complex, but the results are simply how nature behaves.

## Time for an experiment

Suppose you made up a hydronic circuit such as the one shown in Figure 1. It contains 50 ft. of residential fin-tube baseboard, along with a variable-speed circulator, flow meter, two temperature gauges and some type of heat source. The heat source is controlled so the supply water temperature into the fin-tube element stays right at 180° F.

You turn on the circulator at full speed and the flow meter indicates 8 gpm. The inlet temperature is steady at 180° and, in a short time, the outlet temperature of the fin-tube element stabilizes at 174°. Knowing the flow rate and temperature drop along the fin-tube, you can calculate the rate of heat dissipation.

See Formula 1.

Where:

Q = rate of heat output (Btu/hr.)

D = density of the fluid (lb./ft.3)

c = specific heat of fluid (Btu/lb./°F)

f = flow rate (gpm)

?T = temperature drop (°F)

8.01 = a number that makes the units correct

Maybe you used the simpler version of this formula:

See Formula 2.

These results are close, but not the same. That’s because the number 500 in the latter formula is based on the density of water at 60°, rather than the density at its actual operating temperature. When water is heated, its density decreases.

Now that you have a reasonable measurement of the heat output at a flow rate of 8 gpm, you reduce the speed of the circulator so the flow rate drops by 1 gpm, wait for temperatures to stabilize and write down the measured flow rate and outlet temperature. You keep doing this for flow rates all the way down to 0.5 gpm.

Then you use this data to calculate the temperature drop across the fin-tube element (e.g., ?T) and its heat output rate.

After you’ve done all this, you graph the results for heat output and temperature drop. They should look like the graphs in Figure 2.

The graph of heat output (q) vs. flow rate is probably not what you expected — especially if you think proportionally. It shows that heat output from the fin-tube element drops off rather slowly with decreasing flow rate, until you get down to about 2 gpm. Then, heat output really nose dives with further reductions in flow rate.

Although it might not be what you expected, it is what it is. This characteristic is shared by all hydronic heat emitters: fin-tube, convectors, panel radiators and even radiant panel circuits. Heat output changes very quickly at low flow rates but very gradually at higher flow rates. This trend also holds true at other supply water temperatures.

Now take a look at the temperature drop across the fin-tube over the same range of flow rates. First, it’s obvious the temperature drop doesn’t remain constant as flow rate changes. The ?T happens to be at the sacrosanct value of 20° when the flow rate is just a bit more than 2 gpm. As flow increases above 2 gpm, the ?T keeps dropping. At 8 gpm, it’s only about 6°. When the flow is only 0.5 gpm, the ?T is slightly above 55°.

These ?T values are the direct result of heat output. Nothing in this setup forces the ?T to stay at any particular value. And nothing is wrong with the fact that ?T is changing. It just goes where nature takes it as we stand by and watch.

## Keeping ‘score’

Do you remember how President Abraham Lincoln’s Gettysburg Address begins? “Four score and seven years ago …” When describing time, a score meant 20 years.

Perhaps we should recognize the quantity 20° as having a special place in the recorded history of North American hydronics. It deserves that distinction, not because of any technical merit, but because it has established an unwavering allegiance among many who design hydronic systems.

I’ve seen this many times. Someone draws a box representing a boiler on a piece of paper. They draw an arrow pointing out of the box and label it 180° F. Then they draw an arrow pointing into the box. Guess what label that second arrow gets? Yep, 160° F. Change the label on the outgoing arrow to 120° and ask for an update on the incoming arrow.

What do you think it’s going to be? My bet is on 100°. It’s as if the water “knows” how to drop 20° whenever it goes around a hydronic heating circuit and then increase by 20° as it passes through the boiler.

I used to joke about this during seminars. My postulation to the audience was as follows: If you want to ensure that your hydronic systems always operate at a 20° ?T, there is a way to do it but it’s complicated and expensive.

First, you have to go to Germany. Then you have to scoop up water from the Rhine River and ship it back to the United States for use in your systems. That’s because the Germans are so smart they have “trained” the water in the Rhine to lower its temperature by 20° if it ever finds itself moving through a North American hydronic heating system.

Most people laugh when they hear this. The scary part is when someone who didn’t laugh comes up during a break and whispers in my ear, “Hey, I want to rep that German water, who should I contact?”

There’s no question the Germans are pretty smart when it comes to hydronics. They’re smart enough to know nothing is special about 20° when it comes to hydronic system design or operation.

## 20 alternatives

It’s common in Europe to see panel radiator circuits designed for design load ?Ts of 30° or perhaps even higher. They do this because it reduces flow rate and reduced flow rate means small pipe and small circulators. It also means lower operating cost. Over there, every watt counts. They won’t operate a circulator at 25 watts if it can create the necessary flow rate at 20 watts. They care and so should we.

Radiant floor-heating circuits also can be designed for different design load ?Ts. I like to design around 15° for floor circuits in areas expected to have “barefoot-friendly” floors. The smaller ?T reduces variation in floor surface temperature a bit compared to what it would be at a ?T of 20°.

However, in an industrial building, I may push the design ?T up to 25° for two reasons. First, heated concrete slabs in most industrial applications don’t need to be barefoot-friendly. Slightly wider variations in floor surface temperature are hard to notice through a pair of Redwing boots. Second, I like the way those Germans think about pipe sizes and circulator wattage.

Will our industry continue to design systems around 20°?

Will the sun come up tomorrow?

My objective is not to dissuade you from designing around 20° ?T at design load. It’s to assure you the sun will come up tomorrow if you happen to pick a different value. And for those who want to stick exclusively to 20° — please, no more phone calls on how to rep that German water.