# A Relationship With Benefits

By JOHN SIEGENTHALER

HydronicsHow flow affects heat output and deltaT.

Unfortunately, nature does not always work in proportions. It takes almost 800 horsepower to produce that kind of speed. Most of that power goes into overcoming the aerodynamic drag of the car at those high speeds.

**NON-PROPORTIONAL THINGS**

Hydronics also has its share of non-proportional relationships. One of them is how the heat output and temperature drop across a heat emitter is effected by the flow rate through it.

For example, suppose a given length of residential fin-tube was yielding a heat output of 5000 Btu/hr when operating at a flow rate of one gpm. 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 hardware every day, would say that heat output would double. That answer might seem intuitive, but it is not correct.

How about if the flow rate were increased from one to four gpm? That is a 400 per cent increase, surely that would at least double the heat output. To answer this, just look at some I=B=R (Institute of Boiler and Radiator Manufacturers) output ratings from baseboard manufacturers. They are given for a wide range of water temperatures and for flow rates of one gpm and four gpm.

You will find the rating at a flow rate of four gpm is about six per cent higher than the rating at one 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. It is also 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.

**MAKING SOME MEASUREMENTS**

Suppose you made up a hydronic circuit like the one shown in *Figure 1*. This circuit contains 50 feet of residential fin-tube baseboard, along with a variable speed circulator, flow meter, two temperature gauges and some type of heat source. That heat source is controlled so that the supply water temperature into the fin-tube element stays at 180F.

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

*q* = rate of heat output (Btu/hr)

D = density of the fluid (lb/ft^{3})

c = specific heat of fluid (Btu/lb/ºF)

*f* = flow rate (gpm)

T = temperature drop (ºF)

8.01 = a number that makes the units correct

Now that you have a reasonable measurement of the heat output at a flow rate of eight gpm, you reduce the speed of the circulator so that the flow rate drops by one gpm. Wait for temperatures to stabilize and then 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 (that is T) and its heat output rate. You then graph the results for heat output and temperature drop. They should look similar to the graph in *Figure 2.*

**THAT IS JUST THE WAY IT IS**

The graph of heat output (q) versus 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 to a flow rate of about two gpm. Below this value the heat output really nose dives as you further reduce the flow rate.

Heat output changes very quickly at low flow rates, but very gradually at higher flow rates. This characteristic is shared by all hydronic heat emitters: fin-tube, convectors, panel radiators, and even radiant panel circuits. 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 is obvious that the temperature drop does not remain constant as flow rate changes. The T happens to be at the commonly assumed value of 20F when the flow rate is just a bit over two gpm. As flow increases above two gpm, the T keeps dropping. At eight gpm it is only about 6F. When the flow is only 0.5 gpm, the T is slightly above 55F.

These T values are the direct result of heat output. There is nothing in this setup that forces the T to stay at any particular value. There is also nothing “wrong” with the fact that the T is changing.

**WHY 20?**

I think that a circuit temperature drop of 20F deserves 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 have seen this many times.

Someone draws a box representing a boiler on a piece of paper. They draw an arrow pointing into this box and label it as 160F. Then they draw an arrow pointing out of that box. Most of the time it will get labelled 180F. Change the label on the outgoing arrow to 120F and ask for an update on the incoming arrow. What do you think it is going to be? My bet is on 100F.

It is as if the water “knows” how to increase by 20F as it passes through any hydronic heat source and then drop by 20F as it passes around any hydronic distribution system. This is not true and it is also not necessary.

It is common in Europe to see panel radiator circuits designed for design load Ts of 30F or perhaps even higher. They do this because it reduces flow rate and reduced flow rate means small pipes and small circulators. It also means lower operating cost. Over there, every watt counts. They won’t operate a circulator at 45 watts, if it can create the necessary flow rate at 35 watts. They care and so should we.

Radiant floor heating circuits can also be designed for different design load Ts. I like to design around 15F for floor circuits in areas that are 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 20F. However, in an industrial building, I may push the design load T for the circuit up to 25F. That is because heated concrete slabs in most industrial buildings do not need to be “barefoot friendly.” Designing around slightly larger circuit temperature drops also reduces flow rate, which in turn decreases circulator size and power require

ments.

In summary, the relationship between the heat output of a hydronic circuit and the flow rate passing through it is not proportional. Neither is the relationship between the circuit’s temperature drop and the flow rate through it. Be sure to examine this relationship as you design future systems. Opportunities abound for reducing both installation and operating costs based on reduced flow rates and higher circuit temperature drops. <>