In engineering, “shock” is defined as a phenomenon that happens when matter is subject to extreme rates of force with respect to time. This is probably one of those engineering concepts that most of us understand without a scientific dissertation. In plumbing engineering, one of the most common forms of shock is water hammer: A phenomenon caused by water moving at a high velocity that stops suddenly. Not only does water hammer cause a problem because of the noise it makes but it can cause piping and fittings to fail prematurely as well.

We should all be familiar with the concept of what happens when something that has momentum gets stopped suddenly. A good example is when you are walking down a busy sidewalk and someone stops in front of you suddenly to check their phone. In the case of water hammer, it happens when a valve is closed suddenly, and this is usually the case with valves that are electrically controlled. This is the case with solenoid valves, which operate when electricity is applied to a winding and pulls in armature. Plumbing codes may require us to design systems with devices that absorb pressure resulting from the quick-closing of valves. The first question then becomes: “What defines a quick-closing valve?”

The PDI Standard WH-201 gives us the answer in the form of a formula. The standard states: “Quick valve closure may be defined as a closure less than or equal to two times the length of pipe divided by ‘a,’ which is the velocity of water pressure wave.” Looking at a pipe run of 40 feet to a bathroom core from a corridor main, the time for a valve to be defined as “quick-closing” would need to be less than:

The important takeaway from this formula is to note the effect that pipe length has on the impact of a solenoid valve. An 80 foot run of pipe would increase the critical response time to 40 milliseconds and include most solenoid valves. The other important takeaway is valves such as quarter-turn ball valves would probably not fall under the category of “quick-acting.”

Plumbing Codes do not always have us look at the piping design for each individual fixture that has a quick-closing valve to determine if it needs a pressure absorbing device or not. It would be a lot for the code to ask and, truth be told, there are many factors involved with water hammer. It is helpful to understand those factors when we size and apply the devices themselves.

Let’s look at the pressure incurred by water hammer for the flow to a water closet through a 1-inch diameter pipe. The only value we need to find is the change in velocity. To do that, we need to first determine the flow rate in gallons per minute. A 1.28 gpf valve will operate in a second or two, which translates to a value of up to 75 gpm. Appendix A-4 of PDI Standard WH-201 has a chart that we can refer to, and shows a velocity of 25 feet per second. The equation for determining the maximum pressure wave is shown below with results from our specific example:

This is somewhat of an extreme example, but not unheard of if the flush valve is adjusted incorrectly — there is high pressure and undersized piping. The pressure wave is what reverberates back through the piping system, causing noise and vibration. On the other end of the spectrum are solenoid valves used on lavatory faucets. The main difference is the flow velocity. Instead of 25 feet per second, we are looking at 0.5 gpm through a 1/2-inch pipe typically, which equates to less than 1 foot per second. Per the PDI Standard, the rule of thumb is that your pressure wave is going to be about 60 times your velocity, so in the case of the lavatory faucet, we are looking at about 60 psi. While this is within the specified range of most plumbing components, the shock may have a deleterious effect on the faucet itself.

Once we have determined that a device is required to absorb high pressures resulting from the quick-closing of valves, we have a couple of ways to size the device required. The simplest way is to refer to the PDI Standard WH-201 which has tables that show the recommended size based on fixture units. There are also tables that provide sizing based on pipe size and length of the run.

The other method is to use a formula. This allows us to look more closely at the parameters that affect sizing. One empirical formula that has been developed is the following:

Where:

C is the required capacity of the arrestor;

L is effective length of pipe;

V is flow rate in GPM;

D is pipe diameter;

Pf  is the flow pressure; and

Y is a ratio based on the maximum design pressure of the piping and the nominal operational pressure.

For a typical domestic water plumbing system, the maximum pressure is 150 psig and operating pressure is no greater than 80 psig per code, so the Y factor is around 2.

Let’s take a closer look at that water closet flush valve that was fed with a 1-inch pipe. For a 40-foot run from the main in the corridor, the required arrestor capacity would be:

Now, this is an extreme example with a very large water hammer arrestor. But one can see how, with improper adjustment and system sizing, things can get out of control. As with most calculations, if you can make the top values decrease or the bottom values increase, you can decrease your result, or in this case, the required capacity. Let’s say the flow rate through a properly adjusted flushometer is actually 25 gpm, and let’s use a 1.5-inch pipe. Instead of 80 psig, let’s say that the design pressure is the minimum that engineers use to operate a flushometer — 35 psig. Our required arrestor capacity becomes:

100 cubic inches is more in line with what you would expect to see for a water hammer arrestor size on a supply to a water closet flush valve. These are more commonly sized by fixture units according to the PDI Standard.

Following the plumbing code and the standards available to us help us understand the importance of preventing water hammer. Look closer at the empirical formulas that were developed through testing help us understand the parameters that affect water hammer. This allows us to troubleshoot situations that may arise in the field.

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