The Power and Elegance of Circles

I’m a lifelong figure skating fan. If someone were to ask me why, the first thought that comes to mind is the power and elegance in it. There is a convergence of power, speed and grace, where these coincide to create the breathtakingly captivating experience we see on the ice. If you’ve ever watched a performance, you’ll quickly see that circular motions are what make the shows. What now? You’re not into figure skating, so you say? Try it, try it, and you may! In that case, let’s get on a race track and rev up your engines. If neither figure skating nor cars are gonna do it for you, so much more is governed by circular shapes that there aren’t enough hours in the day to cover it.

  • For those of us involved with water stewardship, circles are everywhere. They are in all places water transport and water treatment. I work in a pump shop. We call it rotary equipment. It’s only in these last few months that circles being in every facet of water stewardship has become a stark observation. It really came together for me in this last week, while I was taking a close look at pump stuffing box drawing. The diameter for gland, shaft, lock nuts, and bearings among other things, are all specified with diameter symbols throughout the page.
  • Some people have visions of sugar plums dancing in their heads. I was looking at the page, seeing nothing but diameter symbols everywhere because each of these components is circular. We wanted to know what it would take to possibly fit a cartridge type mechanical seal into the tight clearance, possibly boring through the box to accommodate a packing-to-seal conversion.
  • In tandem, I was overhearing an inquiry for a sump basin diameter. I walked out into our shop and looked at the wall of gaskets, baskets of o-rings, and shelves of couplings, pipes, fittings, impellers, and yes, at FRP basins being prepped for pump station installations. It was this unreal recognition. There are just circles, circles, and nothing but more circles all over the place. You have to leave the shop to get away from them, even for one moment! When calculating new installations and retrofits, this has implications for how it’s done.

If we know a diameter, calculating a circumference is straightforward. Here are some basic definitions:

  • Radius: A straight line extending from the center of a circle to one end of the circle (diameter / 2).
  • Diameter: A straight line across the center of a circle, from end-to-end (2 * radius, since a radius is half of a diameter).
  • Circumference: The linear distance around the circle. (2 * pi * radius), or (pi * diameter).
  • pi: A little over 3x the diameter of a circle. 3.14….

Why are there so many circles in the structures of water stewardship? It turns out that circles are the most efficient shape for handling pressure because pressure force is evenly distributed around a circumference. With other shapes, pressure forces concentrate at the corners, requiring expensive non-standard inefficient reinforcement. So, let’s say we have flow through a square. Is the velocity the same or is it slowed down? Well, if pressure is not evenly distributed, it can’t accelerate the same.

  • From the above example, we know that circumference is (2 * pi * radius). For circular motion, here’s how it’s determined:
  • Average speed = distance/time = (2 * pi * radius)/time. In other words, circumference is the distance we’re talking about here divided by time, which gives us the average speed.

I’ve been talking about circles in terms of their mechanics. Bacteria and other buildup such as scaling also love to hide in corners and crevices that come from shapes other than circular. This, too, means circles are a winning shape.

All of this had me curious about the larger picture above and beyond water. Circles are elegant and the most powerful of any shape to be found in the universe and beyond. They might be the shape of choice in water stewardship, but they didn’t start there. That shape is found everywhere in nature, and its use in water stewardship is simply a mirror to it. Everything from atoms to cells to the earth, planets, sun, moon, and even black holes are all circular shapes. It’s only fitting that the shape of the basic building block of life is also the best conductor to what flows through it.

That’s fascinating. And beautiful.

Close the Loop on Power!

Volts, amps, watts, kilowatts, and power. I don’t know about you, but until today, nothing has earned my ire and frustration quite as much as trying to clearly understand the difference between these electrical terms once and for all: volts, amps, watts, kilowatts, and power. They’re all to do with electricity, but what exactly do they each mean, and how do they all fit together? Today is the day for closing this loop!

A practical example involving all of these terms makes it easy to grasp them. Let’s say we have a motor with a dual rating of 230V/460V. Will running a motor at its higher voltage rating save money by using less amperage?

It won’t because we pay for power in watts or kilowatts. Volts are units measuring electrical potential, while amps are a unit of measurement for electrical current. Power is the combined value of amps (electrical current) and volts (electrical potential), and it turns out be the same for each “rated value” (meaning the 230V or 460V voltage values rated to the motor on its nameplate). Power, which is (amps * volts) is measured in watts or kilowatts.

So, for example, if we’ve got:

*14 amps run at 230V, (14 * 230) that’s 3,220 watts, or 3.2 kw of power

*7 amps run at 460V (7*460) is also 3,220 watts, or 3.2 kw of power

What’s interesting to note is that the higher voltage rated value of 460V is double that of the lower value of 230V. It takes half the amps (i.e., running electrical current) to get the same power (measured in watts or kilowatts) with 460V (of electrical potential) to attain 3.2 kw of power.

Running current at the higher rating can only save money on installation costs because smaller diameter wires can be run at the higher rating than are required for the lower rating.

This explanation, which I was lucky enough to stumble on in web research, finally had each term making clear sense, while showing how it all fits together in practical terms.

This is the source article via El Paso Electric:


Thermodynamics in Cavitation

I’m not sure I ever really understood the underlying dynamics involved with hydraulic or liquid cavitation until now. I only knew that it involves pressure and equipment damage potential. Thanks to the common sense writing in Mike Volk’s publication, Pump Characteristics and Applications, it finally makes sense. Let me start by saying that there is no way to grasp this topic without learning something totally new to a lot of us.

Cavitation involves vapor pressure creating bubbles that collapse in implosion. I kept seeing images of bubbles headed toward pump impeller eyes in various books with the caption: “cavitation”. That was a start in the right direction in grasping this. It turns out that actually getting it means learning a little about thermodynamics. Those bubbles are boiling water! Now, wait a minute. How can that be? We are talking about ambient temperature water that is boiling, not high temperature water over a stovetop.

If you’re like me, you might have only known about raising temperature as a means to get liquid boiling. This is where it gets interesting. There is another way to get water or another liquid boiling starting with a lower or even ambient or cold temperature, and that is to lower pressure below vapor pressure. I was reading this in awe because I’ve gone through life without this fascinating and useful information. It turns out that pressure and heat are correlated. Raising or lowering either of these, pressure or temperature, has a direct impact on when cavitation happens.

I’ll use a few examples from Mike Volk’s book in my own words on this. So, if we’re talking about 14.7 psia, which is baseline sea level atmospheric pressure, water boils at 212 degrees F. That sounds familiar so far. Now, let’s go climb a mountain where the psia is lower than sea level atmospheric pressure and boil water via raising temperature at that higher level elevation. Water will actually boil at several degrees lower than 212 F, so that means the temperature level is relative to pressure level.

Now, let’s take the psia in the other direction. Let’s say we have 100 psia with a 300 degree temperature. That liquid will not be boiling at 300 degrees with that higher psia. Incredibly, it will just remain in a liquid state. You need to raise the temperature higher to get boiling in that case, and this is how pressure cookers work. Drop the pressure to 67 psia on it and it will boil. At 60 degrees F, vapor pressure is 0.2563 psia, so if pressure is dropped below that, cavitation results. That boiling water with vapor bubbles collapsing and imploding throughout equipment in a significant pressure drop situation even at ambient temperature causes cavitation!

There are predictable causes for water pressure dropping below vapor pressure in equipment such as a pump. Those causes for pressure loss are a topic for another time. And, I’ve been talking about water here. This topic applies to any liquid. If it’s liquid other than water, specific gravity needs to be factored in and taken into account. Thanks for reading!

Why flow coefficient in valve selection matters

Happy New Year and welcome to my first official learning blog post! Couple my current interest in water strewardship with my inherent love for writing, and it should come as no surprise that I’m ringing in the New Year with a blog of my own. I’ve benefitted so much from the blogs of others. Here is my small part and piece to add to it all from the perspective of a relatively new learner.

In the world of pumps, pipes, and valves that I’m in these days, there is a question of how to size a valve for a process system allowing for optimal performance. Undersizing valves can mean restriction upstream and back pressure buildup which can lead to flashing or cavitation. Oversizing via a too large flow/valve coefficient can lead to the opposite problem: a drastic pressure drop and velocity speed up. Here again, there is the real chance of encountering flashing or cavitation. Trim parts inside a valve can start eroding, causing a “bathtub stopper effect” wherein the closure element of a valve gets sucked into its seat. 

What are flashing and cavitation? These are pressure problems at opposite ends of each other, both with real potential for damaging effects to anything in their paths. When we’re thinking about the concept of pressure, it has to due with a strong or weak flow of water.

  • With high pressure, i.e. low/weak water flow, we want to boost water flow up to meet demand.
  • It is the opposite with strong/high water flow. We need to do the opposite and decrease it.
  • Too fast of a velocity or speed boost of the water flow results in a large pressure drop. A large pressure drop can lead to flashing, whereby water “flashes” into a partially vaporized state with the potential for equipment damage.
  • Slow the speed, i.e. velocity, down too far and we get a large pressure increase. This is where cavitation comes in. Now we have too much pressure, so we’ve got water static pressure dropping below vapor pressure instead. The vapor evaporation collapses on itself and that’s cavitation. Think of caved in or deformed pipes, valves, or equipment and you’ve got the idea here.

This, in part, all has to do with the valve “restriction”. What is restriction? Drumroll, please…

You say you’ve gotta valve in the path of a pipe, do you? Drumroll square roots, because they are all over this and so many other of these doggone mechanical engineering problems. There is an equation called the “Square-Root Law”, whereby flow = restriction * square root of pressure drop. I need to figure out how to get these symbols in my posts properly. Until then, there are calculators and charts that punch these out in no time.

Back to where we started here: valve coefficients. There is a sizing formula for this, known as Cv. Cv = flow * square root of (specific gravity/pressure drop).  Don’t get hung up or caught up in this. And please don’t let anyone try to say that you *just can’t* possibly understand or grasp this due to it being formulaic. Everyone uses calculators. Get your hands on one and you’re as good to go as anyone else making this proclamation. They’re not doing anything else we wouldn’t.

We need to get this right to size valves properly to optimize performance and avoid expensive wear and tear. Flow characteristics come into this, where there are inherent flow and installed flow characteristics. WTH, you might ask. I know I did. Inherent flow does not take into account the effects of piping, while installed flow does. There is more to this, but I am putting a close to this post for now. Thanks for reading. Please feel free to add or comment. Where is the rest of the topic here? I’m not done yet! If there is interest, please stay tuned for more.

All my best wishes for health, happiness, and exciting new learning and development in the New Year!

In gratitude,

Jennifer Zadka

Good company in a journey makes the way seem shorter. — Izaak Walton