Is the water moving too fast?

One question about hydronic heating that pops up over and over again is this: If the 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? The answer, from the standpoint of heat transfer alone, is no. But rather than just take my word for it, let’s see why this is true.

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.

The surface contact area, the temperature difference between the fluid and the wetted surface, and the convection coefficient, govern convection. The latter can be estimated using 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 do not 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 of the flow stream, they give up heat to the tube wall and cool down more than fluid molecules 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.

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 one gallon per minute (gpm) and four gpm. The output at four gpm will always be slightly higher than at one gpm (all other conditions being the same).

Years ago, the Hydronics Institute in the U.S. developed the following formula for estimating the increased heat output of fin-tube baseboard for flow rates above one gpm.

  Q_f=Q₁x(f^0.04)

Where:

     Q_f = heat output at flow rate f (Btu/hr/ft)

    Q₁ = heat output at flow rate of 1 gpm (Btu/hr/ft)

      f = flow rate through baseboard (gpm)

0.04 = exponent

Here is an example: Assume the rated heat output of a fin-tube baseboard is 550 Btu/hr/ft at 180F water temperature and flow rate of one gpm. Estimate the output of this baseboard at a flow rate of five gpm and the same 180F water temperature.

Q_f = Q₁x(f^0.04) = 550x(5^0.04) = 550x(1.066) = 587 Btuh/ft

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 one to four gpm only increases heat output about six per cent.

Next, go look up the output ratings for fan- or blower-equipped convectors. Just in case you do not have a catalogue handy, the output of a small wall convector operating at a fixed inlet water temperature is plotted in Figure 3.

Once 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 will also find heat output increases at higher fan speeds. This occurs for the same reason as on the water-side of the heat emitter; faster flows reduce the thickness and thus the thermal 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 four-inch bare concrete slab. The supply water temperature is 110F. The only thing that is changing 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 flow rates. At 0.2 gallons per minute, only 10 per cent of the maximum flow rate shown on the graph, the circuit releases about 44 per cent of the maximum heat output. Increasing flow from one to two gpm only increases heat output about 11 per cent.

THE OTHER SIDE OF THE STORY

Hopefully you are 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 that needs to be considered when designing hydronic systems. Issues such as head loss, piping erosion and system operating costs 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 sharply increased operating cost. Any time 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 is an example of how quickly that operating cost can climb as flow rates are increased.

Take the 250-ft. by ½ in. PEX floor heating circuit previously discussed. Operating at one gpm and 110 F supply temperature, this circuit releases 7117 Btuh. Bumping the flow rate to two gpm with the same supply temperature increases heat output to 7902 Btuh (a modest 11 per cent increase).

The circuit’s head loss at one gpm is 9.98 ft. The pressure drop corresponding to this head loss is 4.3 psi. Assuming a small wet-rotor circulator operating with a wire-to-water efficiency of 25 per cent provides flow and head, the electrical power needed to operate this one circuit can be calculated as shown in Formula 2 (at right).

Where:

     W  =  required electrical power input to circulator (watts)

      f  =  flow rate (gpm)

     P  =  pressure drop (psi)

0.25  =  assumed wire-to-water efficiency of circulator (decimal per cent)

Assuming the circuit operates for 3000 hours a year in an area where electricity costs $0.10/kWhr, the annual electrical operating cost of this single circuit is $2.24, probably less than you paid for your last hamburger.

Now, let’s double the flow rate through the circuit to two gpm. The circuit’s head loss climbs to 33.58 ft. 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 annual cost to operate this circuit at two gpm rather than one 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 four per cent per year, the total added operating cost is staggering.

 C_T = C₁x{(1+i)^N-1/i} = $127.6x{(1+0.04)²⁰-1/0.04} = $3,800

Where:

     C_T  =  total operating cost of a period of N years ($)

     C₁  =  first year operating cost ($)

      i  =  inflation rate on annual cost (decimal per cent)

     N  =  number of years in life cycle

Spending $3,800 more in electricity to achieve an 11 per cent boost in heat output (with a corresponding 11 per cent added fuel required to produce this heat) just does not make sense.

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 four feet per second to avoid potential erosion issues. This corresponds to the velocity limit often imposed to avoid objectionable flow noise for pipes routed 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 four feet per second.

Figure 5 lists the flow rates corresponding to flow velocities of four 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 two feet per second. These minimum flow rates are recommended to provide air bubble entrainment.

THINK AVERAGES

Finally, if you still think the water can move too fast for the heat to jump off, consider the following situation as a practical rationale that this is not the case.

A fin-tube baseboard is operated at three different flow rates, but with the same 180F entering water temperature, and the same surrounding air temperature (see Figure 6).

At the low flow rate the temperature drop across the heat emitter is 20F and thus the average water temperature in it is 170F. When flow is boosted to the medium level the outlet temperature rises to 170F and hence the average water temperature inside the heat emitter is 175F. Finally, when the flow rate is boosted to the high level, the outlet temperature of 178F is a mere 2F below the inlet temperature. The average water temperature is 179F. 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 is just no way around the physics of this situation.

SAY IT AIN’T SO

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 has been discussed here to convince them otherwise. Also, be sure they understand the consequences of excessive flow rates. Hundreds and even thousands of dollars are usually at stake.

John Siegenthaler, P.E., is a mechanical engineering graduate of Rensselaer Polytechnic Institute and a licensed professional engineer. He has over 34 years experience in designing modern hydronic heating systems. Siegenthaler’s latest book, Heating with Renewable Energy, was released last month (see p55 in the digital edition at www.hpacmag.com, or visit www.hydronicpros.com for more information).