# Expanded Thinking

A scientist would probably argue over the word practically in the previous sentence. They would correctly point out that water can indeed be slightly reduced in volume under several thousands of psi. But us “purveyors of the pipe” know that long before our systems ever reach such pressures, their relief valves will have opened, or the buildings they serve will have been launched into the next county.

The fact that water is practically incompressible means that any container completely filled with water, deaerated and sealed, will experience a very significant rise in pressure when the water undergoes a rise in temperature. A closed-loop hydronic system is such a container. If pressure variations are to remain manageable, the system must include a properly sized expansion tank. This month’s column summarizes the sizing of a modern diaphragm-type expansion tank.

A diaphragm-type expansion tank is a thin-walled steel pressure vessel that contains a flexible membrane totally separating system fluid from a captive volume of air. As the system fluid is heated, its extra volume is pushed into the tank, which in turn compresses the air on the other side of the diaphragm. Because air is compressible, its pressure rise is much easier to accommodate. Essentially the expansion tank converts what would be a very large pressure change of an incompressible liquid into a much smaller pressure increase of a compressible gas.

Check The Tires: To use a diaphragm-type expansion tank to its full potential, it’s important that the air side of the diaphragm is fully expanded inside the steel shell before the system fluid begins to expand. Not doing so wastes space in the tank by allowing water to occupy part of the tank’s volume before its temperature begins to rise. Figure 1 depicts the situation.

Ensuring that the diaphragm is fully expanded is easy. First, determine what the water pressure will be at the inlet of the expansion tank before any heating takes place. Use Formula 1 to calculate this pressure. Next, use an accurate pressure gauge and air pump to set the air side pressure to the value before filling the system with water. Most tanks ship precharged to about 12 psi.

where:

Pa = the correct air side pressure, in psi (before adding water to the system) H = the height of liquid in the system above the inlet to the expansion tank (in feet) Dc = the density of the system fluid at its initial (cold) fill temperature (in lb/ft.3) 5 = an allowance for 5 psi static pressure at top of system (for air vent operation)

Formula 1 is set up so it can be used for systems containing either water or antifreeze solutions. It requires the density of the “cold” fluid used to fill the system. For water, use a value of 62.4 lb/ft.3. For other fluids look up their density at 60 degrees F in manufacturer’s technical literature. The number 5 at the end of the formula assumes that 5 psi of static pressure is desired at the top of the piping system to help push air out through vents, as well as to suppress vapor pocket formations in high temperature systems. This number can be adjusted up or down, but be warned that higher values will result in larger expansion tank sizes. The value H in the formula is simply the vertical distance from the inlet of the expansion tank to the top of the piping system (in feet). The greater this height is, the greater the static pressure on the tank and thus the higher the air-side pressurization required to fully expand the air side of the diaphragm.

The next step is to estimate the system’s fluid volume. The more fluid in the system, the greater the expansion volume needs to be. System volume can be approximated by first estimating the length of each copper tube size used in the system, and then applying the data in Table 2. For other pipe materials the internal volume (in gallons per foot of pipe) can be found using Formula 2. The volume of other components such as the boiler can usually be found in manufacturer’s data.

where: d = internal diameter of pipe (in inches)

Now you’re ready to plug numbers into Formula 3. The math builds in the assumption that most relief valves will start “dribbling” 2 or 3 psi below their rated opening pressure. In effect, the expansion tank is sized so that at maximum system temperature the pressure at the relief valve is 5 psi less than the valve’s rated opening pressure. This safety factor also allows for the possibility that the relief valve may be 3 or 4 feet below the expansion tank connection and thus subject to a slightly higher static pressure. You’ll also need an estimate of the fluid’s density when it’s up to maximum operating temperature. For water, you can read this from Figure 3. For antifreeze solutions, you’ll again have to refer to manufacturer’s literature. The end result of this calculation will be the minimum required expansion tank volume, in gallons.

where:

Vt = the required minimum volume of the expansion tank (in gallons) Vsystem = the system volume (in gallons) PRV = the rated pressure at which the pressure relief valve opens (in psi) Pa = the correct air side pressure (in psi) Dh = the density of the system fluid at its final (hot) temperature (in lb/ ft.3) Dc = the density of the system fluid at its initial (cold) fill temperature (in lb/ft.3)

For example, say the top of a piping system is 20 feet above the expansion tank connection. The system is filled with water at 60 degrees F. Based on the amount of piping and boiler volume, it’s estimated the system contains 22 gallons of water. The boiler is equipped with a 30 psi relief valve. The maximum operating temperature of the system will be 200 degrees F. What is the minimum expansion tank volume required?

Solution: The air side pressurization is calculated using Formula 1:

From Figure 3 the density of water at 200 degrees F is about 59.9 lb/ft.3 Putting the numbers in Formula 3 yields:

Remember this in the minimum expansion tank volume required based on the previous assumptions. Using a larger volume tank is fine. Doing so will further reduce the variation in system pressure between its temperature extremes, albeit at a higher installed cost.

Points Worth Pondering: This sizing method is conservative since all the fluid in a hydronic system is never at maximum operating temperature at the same time. This means the total expansion volume of a real system — one operating with a temperature drop in the distribution piping — will be slightly less than predicted. This is especially true of large floor heating systems that contain high temperature fluid in the boiler and near boiler piping, but simultaneously hold the majority of their fluid within thousands of feet of embedded tubing that only sees a fraction of the temperature change of the boiler. For such cases, the above procedure will tend to oversize the expansion tank. To trim the fat a bit use Formula 3 twice. Once for the sub-system that represents volume and temperature change of the boiler and near boiler piping (up to the mixing device) and then a second time for the volume and temperature change of the low temperature part of the system. Add the resulting volumes together to get the minimum volume of a single expansion tank for the entire system. Remember to use Formula 1 to calculate the value of the air side pressure (Pa) for the tank mounting location, and then use that value in both calculations of Formula 3.

It’s difficult to imagine that any regular reader of PM wouldn’t know this by now, but it’s worth stating again: It’s always preferable to locate circulators so they pump away from the expansion tank. This allows the differential pressure created by the circulator to be added to the static pressure in the system, reducing the risk of cavitation and expediting air elimination.

Another often overlooked quirk is heating of the expansion tank shell due to its proximity to hot system components. An example being a system where the tank is screwed directly into an air separator near the discharge of the boiler. Conductive heat transfer to the shell raises the temperature of the air inside the tank and increases its pressure. The result can be a wider variation in system pressure. Given the above calculations tend to oversize the tank anyway, this extra heating has not — at least in my experience — been a major problem.

Still, a cooler tank is a happier tank, and probably will return the favor in the form of longer diaphragm life. Tank heating can be minimized by installing a length of connector piping between the tank and the system connecting point. Dropping the tank a couple of feet below the system connecting point is OK, but keep in mind it increases the static pressure and reduces the tank’s effective pressure range. Ideally, the connector piping would drop down and then return up to form a thermal trap between the tank and the system connecting point.

Finally, don’t assume that a tank sized with water as the system fluid is big enough should antifreeze be added to the system. Glycol/water solutions expand more than water for the same temperature change. The higher the percentage of glycol, the greater the expansion volume. Using the densities of the antifreeze solution in Formulas 1 and 3 will properly account for these differences.