I took an astronomy class once in college that I found to be extremely interesting. Still, it could have been one of those courses of study where people react, “How would anyone ever make a living with astronomy?”

I remember learning about how astronomers can determine the age of a star by analyzing the light waves through a gas spectrometer. I can’t tell you for sure how people who study astronomy make a living, but I can say that the class instilled awe and wonder within my own mind about the science of the galaxy.

Long before I studied engineering, I was in awe of water. Memories about water include feeling the power of an ocean wave, admiring a water feature in the park or walking on a frozen pond. In plumbing engineering there is an aspect that is arguably nonscientific, that begs us to use our intuition, and pon-der the behavior of the systems we design. Just as astronomers gaze at the stars for inspiration and then apply their science to unlock the secrets of the universe, us plumbing engineers can look at the mysteries of water and apply our engineering skills to design systems for the spaces we live in. While the foundation of astronomy was built by scientists such as Copernicus, Galileo and Newton, one name stands out in the field of plumbing engineering: Bernoul-li.

I worked with a plumbing engineer who would turn to Bernoulli’s equation to solve day-to-day problems in our office. At the time, I thought it was a little “ex-tra.” To be honest, I think I was a little jealous that he understood the formula well enough to use it in everyday applications. If you happen to be one of those engineers, I expect to keep hearing from you with corrections to the formulas in my articles.

The Bernoulli equation, as expressed in the ASPE Plumbing Engineering Design Handbook, Volume 1 is:


The way I understand the formula is that hydraulic energy is made up of three components. The first one is height: . After some research, I discov-ered that g and gc are basically the same thing, but just put in the formula as a unit conversion so everything comes out in the wash. So, the takeaway is that Z equals height, or the potential energy.

The other two components of the equation are the ones that are more puzzling to me. How do we put them in context of the work we do and our every-day experiences? Anyone who has been knocked down by an ocean wave, or tried to swim against a river current can understand the power of moving wa-ter. is the component of the Bernoulli equation with the velocity component in it, so if I just plug in the velocity of a wave, the equation should tell me something, right? As I was researching the idea of kinetic energy, I realized it is usually expressed as with mass included. I also learned that the imperial units for kinetic energy is foot-pounds.

Going back to our wave at the beach, I’m thinking the wave travels about 10 feet per second. I came to this estimate based on experience of telling peo-ple over the years “Hey, watch out!” One second is just the amount of time for someone to turn around as the wave tumbles them around as if they were in a washing machine. Next, I need to estimate the mass of the wave. If I imagine the cross section of the wave as a triangle and give it some depth equal to the average width of a body, I come up with around 9 cubic feet. So, the energy transferred from that 4-foot wave as it smacks you head-on would be around:

formula 2

That’s a good slug of water, and as we may remember, one of those obscure units from the Imperial system is indeed the slug, defined as the “mass of some-thing accelerated at a rate of 1 ft/s2 when a force of 1 pound is acted upon it.” I feel pretty good about my calculation and empirical understanding of the third term in the Bernoulli equation. I’ve been tumbled around by some good size waves, and it does indeed feel like wrestling with an 800-pound gorilla.

The second term, deals with the pressure in the system when the water is not moving. It’s also known as pressure head and considers the density of the fluid in the system. One story that comes to mind is when I was learning about pumps. An engineer told me a story about someone who got injured while working around some low-head municipal transfer pumps. The pumps were designed to transfer water about 20 feet of head out of a reservoir. My colleague, Doc, explained to me that a flange bolt had failed and became a projectile. While I was surprised that a pump with only 20 feet of total dynamic head could hurt someone, Doc explained that the force acting on a 36-inch diameter pipe flange can be quite large when you multiply the pounds-per-square-inch times the cross section of the pipe. Twenty feet of head is a little less than 10 pounds per square inch, and a 36-inch pipe has a cross section of around 1,000 inches. That translates to a force of 5 tons!

formula 3

When we think about the three terms in the Bernoulli equation, we can see how they balance each other out. “Still waters run deep;” A river with a large cross section has a low velocity. As the landscape narrows, the energy in the river changes and the velocity increases. This is another example of how the pressure and velocity balance each other.

As we look to the stars and think about how far away each of them may be from one another or how much longer they have to twinkle, we should re-member the things that inspire and help us engineer dependable systems and innovate new ideas.

Go and catch that wave of inspiration