Ethan Grossman: 55 saves lives
A series of stories that borrow from daily life experiences to illustrate engineering concepts.
In 1974, a federal law was passed that limited the speed limit of cars to 55 miles per hour. This was in response to an oil crisis in 1973.
The idea was that limiting the speed at which we drive would reduce gas consumption. The law was repealed in 1995 in favor of letting states set their own speed limits.
Plumbing engineers also must consider and be familiar with a different type of speed limit, the velocity of water flowing in the piping networks we design. In Plumbing engineering, we not only have to consider the consequences of flowing water too fast, but too slow.
For plumbing systems that are pressurized and running full, the maximum recommended velocity is 8 feet per second. This velocity is based on practicality and the laws of physics. The recommended maximum velocity is lower for hot water piping. Designs over 8 feet per second will exhibit turbulent flow, which will result in excess noise and pressure loss. Another concern regarding flow velocity is stagnation. If we design piping that is too large, the flow velocity will be so low that biofilm can start to grow on the piping wall. Good supply piping design is kind of like walking: 8 feet per second translates into an 11-minute mile, which is basically a brisk walk. Exceed that speed and you might end up winded, unless you are a runner.
For plumbing systems that flow by gravity, the important velocity to maintain is on the low end, and is referred to as “scouring velocity.” It is defined in the ASPE design guide as 2 feet per second. Scouring velocity will help assure that solids don’t settle in the pipe and build up over time. Additional recommendations for scouring velocity include designing kitchen waste piping for a minimum flow of 4 feet per second, and for storm water piping to be designed for 3 feet per second. One of the main problems with undersizing gravity drainage pipe is that high velocity can siphon out traps.
Under-sizing piping is obviously a problem because the system may not work. Toilets won’t flush, pumps won’t circulate or you may get backups on drainage. Chances are that you will hear about it soon after the job is built. Oversizing your pipe system might feel right because it is the conservative thing to do, but it could add unnecessary cost to the job and be a substandard design for other reasons.
Do the math
The equation for calculating the velocity of water flowing in supply piping appears fairly straight forward, except that we need to follow up with the unit conversions. The formula, as prescribed in the ASPE design manual is:
As a practical example, let’s say we want to fill a 5-gallon mop bucket in one minute. Is a 1/2-inch pipe big enough to supply that hose bib and stay under 8 feet per second?
We’ve been talking about velocity in feet per second. How the heck do we get there from gallons per minute and square inches? The first thing we need to do is convert 5 gallons per minute into cubic feet per second. After you’ve done this conversion a few times you’ll remember that 1 cubic foot equals 7.48 gallons of water. Unless you live in some sort of science fiction reality, it is commonly known that there are 60 seconds in a minute, all day long. Now we can do the conversion for the flow rate, Q :
The next step is to convert the cross-sectional area of the pipe from square inches to square feet. Using the equation for the area of a circle, we get:
Now that we have completed our unit conversions, we can go back to our first equation that looked so simple and answer the initial question: What is the velocity of water flowing through a 1/2-inch pipe at a rate of 5 gallons per minute? Velocity equals flow divided by the cross-sectional area of the pipe:
“Why did you place an exclamation mark after the answer?” you may ask. The reason is because ever since I began working as a plumbing designer, I was taught to feed wall hydrants with a 3/4-inch pipe. I think I will continue to do so. Someone may want to fill that 5-gallon bucket more quickly.
Methods for calculating the flow velocity in drainage piping is interesting because the equation itself looks more intimidating, but we don’t have to worry as much about complicated unit conversions. The three variables we need to know are: A roughness coefficient, the hydraulic radius of the pipe and the slope of the pipe. The most common equation we use, as referenced in the ASPE design handbook, is the Manning formula, attributed to an Irish engineer named Robert Manning who helped advance the equation in 1890:
If you endeavor to perform the above calculation, you will likely need to look up the Manning coefficient. At that point, you will see that there are numerous tables and nomographs showing velocities and flow rates. I encourage you to explore this information and see how changing slope in your design will help achieve a minimum scouring velocity.
Just as the National Maximum Speed Law was repealed in 1995 to allow states to set their own speed laws, individual plumbing engineers must know what velocity water is designed to flow through the systems they design.
When we drive a car, we need to be aware of everything around us. Plumbing engineers need to be aware of the effect velocity has on piping systems. These effects may include: Stagnation, noise, pressure loss, pump sizing, minimum flow through mixing valve, heat loss through insula-tion, water hammer effect, erosion of piping, scouring of drainage pipe and “drain carry.”
Take it too slow and you may get people zooming by you with random gesticulations; go too fast and you might get pulled over.