New perspectives on a long-standing question. Figure 1

One hydronic heating topic that seems to get endless debate centers on this question: If water moves too fast through a hydronic circuit, will the heat it holds be unable to “jump off” as the stream passes through a heat emitter?

I wrote a PM column addressing this topic back in June 1997, "The Water's Moving Too Fast!" It gave several examples to support why, from the standpoint of thermodynamics, the faster the water moves through any type of hydronic heat emitter, the faster it releases heat into a space. If interested, you can find this article in the PM archives at www.pmmag.com (Free registration required for archived articles.)

It’s been almost 10 years since that column appeared, and this topic still comes up frequently and often elicits strong opinions. Perhaps it’s time to revisit the subject, only this time from a wider perspective.

## Convection Counts

The heat output from any hydronic heat emitter is governed by all three modes of heat transfer. For example, before a radiant floor can release heat into the room by thermal radiation and to a lesser extent natural convection, that heat must pass through the floor materials and tube wall by conduction. Before this happens, the heat must pass from the fluid stream to the tubing wall by convection. Thus, heat output from a radiant floor or any other hydronic heat emitter is dependent on the convective heat transfer between the water stream and inner wall of the heat emitter.

Convection is governed by the surface contact area, the temperature difference between the fluid and the wetted surface, and a number called the convection coefficient. The latter is usually arrived at by complex calculations dependent on variables such as the physical properties of the fluid, geometry of the surface, and the speed of the fluid.

But you don’t have to be a math wizard to understand how the process works. Instead, picture flow moving along the inside of a tube, as shown in Figure 1. A thin “boundary layer” of fluid creeps along the inner wall as the bulk of the fluid moves at higher speeds down the “core” of the flow stream.

Because fluid molecules in the boundary layer do not aggressively mix with those in the core, they give up heat to the tube wall and cool down relative to those in the core. This limits the rate of heat transfer to the tube wall, especially if the flow is laminar rather than turbulent. You could even think of the boundary layer as a thin layer of “liquid insulation” between the heat contained in the core of the flow stream and the cooler tube wall.

The higher the flow rate through the tube, the thinner the boundary layer, and the less it restricts heat transfer between the core and the tube wall. Thus, all other things being equal, higher flow rates always increase convective heat transfer, and this boosts heat output for any hydronic heat emitter. Figure 2

## Check It Out

You can see this effect in the thermal ratings for many types of heat emitters. For example, the heat output of fin-tube baseboard is often listed for arbitrary flow rates of 1 gpm and 4 gpm. The output at 4 gpm will always be slightly higher than at 1 gpm (all other conditions being the same).

The Hydronics Institute developed the following formula for estimating the increased heat output of fin-tube baseboard for flow rates above 1 gpm. ## Formula 1

Where:
Qf = heat output at flow rate f (Btu/hr./ft.)
Q1 = heat output at flow rate of 1 gpm
f = flow rate through baseboard (gpm)
0.04 = exponent

For example, assume the rated heat output of a fin-tube baseboard is 550 Btu/hr./ft. at 180-degree F water temperature and flow rate of 1 gpm. Estimate the output of this baseboard at a flow rate of 5 gpm and the same 180-degree water temperature. ## Formula 2

The graph in Figure 2 shows how this formula estimates the heat output of baseboard at flow rates up to 10 gpm. Although there is a definite increase in heat output with increasing flow, the magnitude of the increase is quite small. For example, increasing flow from 1 to 4 gpm only increases heat output about 6 percent. We’ll discuss this more later on.

Next, go look up the output ratings for fan- or blower-equipped convectors. In case you don’t have a catalog handy, I plotted the output of a small wall convector operating at a fixed inlet water temperature in Figure 3. Figure 3
Again you find that increasing the flow rate through the coil increases heat output. As was the case with baseboards, the increase is slight at higher flow rates. You’ll also find heat output increases at higher fan speeds. This occurs for the same reason discussed with the water side of the heat emitter; faster flows reduce the resistance of the boundary layer between the bulk air stream and the surface of the coil.

How about radiant floor circuits? The graph in Figure 4 shows the upward heat output of a 250-foot long circuit of 1/2-inch PEX tubing embedded at 12-inch spacing in a 4-inch bare concrete slab. The supply water temperature is 110 degrees F. The only thing being varied is flow rate.

Increased flow rate again results in increased upward heat output. The gains are much more noticeable at lower flow rates than at higher flows. At 0.2 gpm, only 10 percent of the maximum flow rate shown on the graph, the circuit releases about 44 percent of the maximum heat output. Increasing flow from 1 to 2 gpm only increases heat output about 11 percent. Figure 4

## The Other Side Of The Story

I hope you’re convinced that the heat output of any hydronic heat emitter increases with increasing flow rate. From the standpoint of heat transfer only, faster flow is always better.

However, heat transfer is not the only thing we need to consider when designing hydronic systems. Issues such as head loss, piping erosion and system operating cost also play a role in selecting flow rates and subsequent piping/circulator hardware. Here is where the downside of high flow velocity becomes apparent.

One very significant drawback to high flow rate is the sharply increased operating cost. Anytime there is flow through a piping component there is head loss, and that head loss has an associated circulator input wattage. Thus, every hydronic component has an operating cost. Here’s an example of how quickly that operating cost can climb as flow rates are increased.

Take the 250-foot by 1/2-inch PEX floor heating circuit previously discussed.

Operating at 1 gpm and 110 degree F supply temperature, this circuit releases 7,117 Btu/hr. Bumping the flow rate to 2 gpm with the same supply temperature increases heat output to 7,902 Btu/hr. (a modest 11 percent increase).

The circuit’s head loss at 1 gpm is 9.98 feet. The pressure drop corresponding to this head loss is 4.3 psi. Assuming flow and head are provided by a small wet-rotor circulator operating with a wire-to-water efficiency of 25 percent, the electrical wattage needed to operate this circuit can be calculated as follows: ## Formula 3

Where:
W = electrical wattage required (watts)
f = flow rate (gpm)
∆P = pressure drop (psi)
0.25 = assumed wire-to-water efficiency of circulator (decimal percent)

Assuming the circuit operates for 3,000 hours a year in an area where electricity costs \$0.10/kwh, the annual electrical operating cost of this single circuit is \$2.24, probably less than you paid for your last hamburger.

Now, lets double the flow rate through the circuit to 2 gpm. The circuit’s head loss climbs to 33.58 feet and the corresponding pressure drop is 14.4 psi. Assuming the same circulator efficiency, the electrical power required to operate the circuit climbs to 50 watts. The annual electrical operating cost for this one circuit using the previously assumed conditions is now \$15.

The added cost to operate this circuit at 2 gpm rather than 1 gpm is \$12.76. Keep in mind this is for one circuit and one year. Assuming 10 identical circuits operating for 20 years with electricity inflating at 4 percent per year, the total added operating cost is staggering! ## Formula 4

Where:
CT = total operating cost of a period of N years (\$)
C1 = first year operating cost (\$)
I = inflation rate on annual cost (decimal percent)
N = number of years in life cycle

Spending \$3,800 more in electricity to achieve an 11 percent boost in heat output (with a corresponding 11 percent added fuel required to produce this heat) just doesn’t make sense. Figure 5

## Wearing Thin

Another effect associated with increased flow velocity is the potential for erosion of copper tubing. According to a report published by the National Association of Corrosion Engineers, sustained flow in copper tubing should not exceed 4 feet per second to avoid potential erosion issues. This corresponds to the velocity limit often imposed to avoid objectionable flow noise for pipes traveling through occupied spaces.

According to one reference, PEX tubing can withstand sustained flow velocities in excess of 90 feet per second at elevated temperatures without damage. However, such velocities are completely beyond the range of practical system design from the standpoint of head loss, flow noise and operating cost. My suggestion is to size PEX tubing for maximum flow velocities in the range of 4 feet per second.

Figure 5 lists the flow rates corresponding to flow velocities of 4 feet per second for common sizes of copper, PEX and PEX-AL-PEX tubing. It also lists the flow rates associated with flow velocities of 2 feet per second. These minimum flow rates are often recommended to provide air bubble entrainment. Figure 6

## Thinking In Averages

Finally, if you still don’t buy into all this stuff about boundary layers, consider the following situation as a practical way to demonstrate that heat output increases with increasing flow rate.

A fin-tube baseboard is operated at three different flow rates, but with the same 180-degree F entering water temperature, and the same surrounding air temperature (see Figure 6). At the lower flow rate, the temperature drop across the heat emitter is 20 degrees F; thus, the average water temperature in it is 170 degrees F. When flow is boosted to the medium level, the outlet temperature rises to 170 degrees F; hence, the average water temperature inside the heat emitter is 175 degrees F.

Finally, when the flow rate is boosted even higher, the outlet temperature is a mere 2 degrees F below the inlet temperature (178 degrees F); thus, the average water temperature is 179 degrees F. In every case, the average water temperature inside the heat emitter increased as flow increased. Increasing the average water temperature inside any heat emitter always increases heat output. There’s just no way around the physics of this situation.

The next time you hear someone lament that their system is not releasing sufficient heat because the water is flowing too fast through the heat emitters, please use what we’ve discussed to convince them otherwise. Also, be sure they understand the consequences of excessive flow rates. Hundreds, even thousands of dollars are usually at stake.