One of the things I love about engineering is remembering those moments that inspire us to keep learning. For me, most of the time, it was related to somebody trying to fix something that was broken.

In a previous article, I wrote about the pumps failing at the crab tank I worked at during High School. That experience stuck with me because I had to sniff all the dead crabs to determine if they were still good to cook or not. A more pleasant experience I had (which was also a more positive olfactory experience) was taking care of a neighbor’s greenhouse when he travelled. He grew orchids and it really was not that big a deal — all I had to do was water them. As he explained to me how the greenhouse worked, he pointed to the roof and explained how wax-filled pistons adjusted roof louvers based on temperature.

This is fascinating to me because it is an example of a thermophysical behavior that we use in one of the most common components we specify in plumbing systems, the thermostatic mixing valve. It is unlike other considerations we must plan for, such as the effect of thermal expansion in piping systems. This is an example where we use a reaction to temperature for our benefit. Most of the time, excess heat or cold is a problem we must deal with. A thermostatic mixing valve uses the change in temperature of water to control the outlet temperature going to fixtures. It does this by extending or contracting a piston that blends the hot and cold water proportionately.

You may recall from the “ASPE Fundamentals of Engineering Design Handbook, Volume 1,” Table 1-1 that lists the thermal expansion coefficient of copper as 9.3 x 10-6 in/in-°F. It is not uncommon for plumbing engineers to calculate the thermal expansion of piping (using equation 1-12 from the “ASPE Fundamentals Handbook”) which is:

equation 1-12 from the “ASPE Fundamentals Handbook”

For the expansion of 100 inches of copper pipe with a temperature differential of 100° F. Using the same formula, we can see that paraffin wax expands at a rate of about 20 times that of copper.

equation2 paraffin

This is one of the reasons paraffin is used for expanding actuators in thermostatic mixing valves. As it expands, it pushes a piston and changes the mixed ratio of hot and cold water automatically. Paraffin wax has a much greater rate of expansion than other materials, especially at the temperatures where we like to have our water delivered for hand washing, showering, washing dishes — you know, all the luxuries in life.

As an aside, because I’m sure it is on everybody’s mind: What happens to those honeybees resting in their hives during the cold? Does all that wax structure just close in on them as the wax contracts? According to research performed by Penn State, honeybee colonies “form a thermoregulating cluster, in which they organize into a tight ball and vibrate their flight muscles to generate heat.” I suppose the simple take away is that if you ever feel like the walls are closing in, just get up and move around.

Another type of mixing valve that uses thermophysical properties is a bimetallic type where two metals with different coefficients of expansion are fused together and bend as the temperature changes.

Plumbing engineers specify and size mixing valves in order to size source equipment and understand flow rates depending on incoming temperatures. The formula to determine the temperature of mixed flow is found in the “ASPE Fundamentals Handbook,” equation 7-1:

“ASPE Fundamentals Handbook,” equation 7-1

For a typical straightforward design in the Northeast, I plan on a worse case of 40° F incoming cold water and 140 °F hot water leaving the water heater. Looking at the proportion of quantity, for a delivered hot water temperature of 130° F at 20 gpm, we would use the hot water ratio formula:

This means of the 20 gpm required, 18 gpm needs to be provided by the water heater.

Up to now, we have touched on one way that temperature is controlled and a method of understanding how much hot and cold water is required. There is another way that mixing valves operate which is through pressure balancing. If you imagine the piston in a thermostatic mixing valve expanding or contracting based on temperature, or a bimetallic type responding to water temperature — these are directly responding to system variations. It is important for engineers and designers to understand that pressure balancing type valves may operate based on spring pressure.

New standards, such as ASSE 1016, require these types of mixing valves to perform in a way that we do not get scalded — or jolted by cold water — when someone flushes a toilet. I’d like to think that those are experiences for years past when you were taking a shower and had to scream out, “Hey, who flushed the toilet?” We should all understand why that used to happen. When a valve was set to control only based on spring pressure, the outgoing water temperature could fluctuate undesirably independent of incoming temperatures.

ASSE 1070 is a different standard relative to thermostatic mixing valves. The tolerances of performance are a little bit tighter than ASSE 1016. As we discussed before, ASSE 1070 valves react more directly to incoming water temperatures. If you want to stay in control under pressure, make sure you understand the basics of how things work; reach out to your local product representative to get even more educated and learn to avoid pitfalls in design. If you really want to stay in control, get involved with organizations that do testing and meet to improve our standards. Together we can learn from each other and continue to improve the industry we all work in.