The Force of Water and Waterjet Technology – Force, Pressure and Flow Volume

By Dr. David A. Summers, Curators’ Professor at Missouri University of Science & Technology

KMT Waterjet Systems Weekly Waterjet Blog

KMT Waterjet Systems Weekly Waterjet Blog

Back in September of 2012, archaeologists found the remains of the last king of England to die in battle. It was Richard III, to whom Shakespeare gave the line “a horse, a horse, my kingdom for a horse!” He died because a blow to his head was focused down to a very high local pressure, even though the overall force of the blow might not have been that great.

Gothic Armor

Figure 1. Gothic Armor of the type worn by Richard III. (Detroit Institute of Arts)

On the other hand, in the middle of Hurricane Katrina, seven years ago, a barge broke through the levee wall above the Lower 9th Ward in New Orleans, LA (NOLA) and released a wall of water that swept through the district. The pressure of the water was quite low, but the overall force it exerted demolished the buildings in its path and swept them off their foundations for eighteen blocks back from the levee. In this case force, not pressure, was the cause of the damage.

Lower 9th Ward in New Orleans

Figure 2. The Lower 9th Ward in New Orleans after Katrina, as the water falls, it flows back into the Industrial Canal. The barge that broke through the levee is on the right. Most of the debris lined the second row of trees back from the levee. (Tulane)

It is this initial relationship between force and pressure and the role that each has to play in the use of waterjets to remove material that form the topic not only for today, but in a number of the posts that will follow. Waterjetting applications now cover a wide spectrum of different uses, and finding the best choice of pressure and flow (which combine to give power) will change from job to job, and hopefully these posts will help make the choice easier.

It is raining outside. As the water drops hit the soil, the water soaks into the soil by penetrating along the existing cracks that exist between the grains of the soil. After a short time the water fills this space, and as it continues to rain, the impact of new rain drops hit the thin wedges of water that now run down into the soil. Although at much lower forces the action is the same as when you hit a wedge driven into a log with a hammer. The wedge pushes the two walls on either side apart, and a crack grows. One of the key elements that give waterjet cutting its advantage is this transformation from an impact force into a pressure, and most particularly a pressure which is applied against all the surfaces with which the water is in contact. It is a point that will be repeated many times.

The stages of soil erosion

Figure 3. The stages of soil erosion – the white arrows in (b) and (c) show the small pressures that are exerted on the particles as additional raindrops keep falling on the water in the ground. This lifts the top two particles in (c) so that the flow of water will carry them away.

With the soil there is not that much material holding the grains together, and so as the rain continues, the soil grains begin to separate from those on either side. Water gets underneath the grains and starts to lift the individual grains free from the mass. Since most land is not flat, the water will now start to flow away under the continued rain, and as it does it carries some of the soil particles that have been freed. This is a simple explanation for the erosion that happens in fields, dirt roads, and other exposed surfaces as they weather. As materials get stronger this process can take much longer to be seen. A high quality stone will erode at the rate of perhaps an inch every thousand years, depending on local weather patterns. There are buildings and bridges built by the Romans all over Europe to prove that point. A weaker granite (and one thinks of the granite in the walls of the Basilica in St Louis as an example) may severely erode within a hundred.

Which brings up an important point: the performance of a waterjet stream is not just controlled by what happens upstream of the nozzle in the delivery system, but it is also affected by the material that it is hitting. And I’ll come back to that in future posts.

First, however, consider what happened during Hurricane Katrina in the Lower 9th Ward. When the barge broke through the levee wall and was carried into the district, it rode on a wall of water that was initially no more than about 30 ft high. We can make a very crude estimate of the pressure of the initial wall of water (neglecting any impact due to the speed at which it moved) based on the height of that wave. A cubic foot of water weighs 62.4 lbs. It sits on an area of 12 x 12 = 144 square inches, so that the pressure under that water is 62.4/144 = 0.43 pounds per square inch (psi). Since that is somewhat close to half-a-psi, as a very simple way of getting the pressure at the bottom of a column of water one can just divide the height in two, and call it psi instead of feet.

So, in the case of that wall of water the pressure at the bottom of the wall would be 30/2 – 15 psi. Since the pressure increases with depth, the average pressure over the height will be half of that, or 7.5 psi. That pressure, by itself, does not appear that powerful.

But when the wave hits a building that pressure is applied over the entire wall. So if the building is 40 ft long and 10 ft high, then the area that sees that pressure is 40 x 12 x 10 x 12 = 57,600 square inches. If that small (7.5 psi) pressure is applied over the whole area, then the force = pressure x area = 7.5 x 57,600 psi = 432,000 lb.

You can now perhaps understand why, when the wave hit the first rows of houses in NOLA that they almost immediately disintegrated, and were carried back as broken debris for about ten blocks.

Aerial view of the Lower 9th Ward

Figure 4. Aerial view of the Lower 9th Ward after the water had drained, and the levee had been replaced. For a sense of scale there is a school bus sitting partially under the barge, and that is the yellow dot at the end of the upper arrow. Each of the flat slabs to the left of the levee marks where a house stood. When we visited the site the house slabs were as shown, but there was still water – and some live fish, standing in the district. (Tulane)

This was a terrible disaster, but there are occasions, particularly in mining, where this terrible force, combining low pressure but high volume flow rates, can be harnessed to do useful work. Such flows are something that our ancestors have known for millennia, and were used as a way of mining from before the age of pumps, and l will tell how they did it in some later articles.

But in most cases we don’t have that amount of water, and the job is more often one where we want to precisely cut a hole, perhaps, in one of the walls of a building, rather than destroying the building. And we haven’t the patience to wait a hundred years to cut through a block of stone. So how do we speed it up? And so we come back to the death of King Richard.

Back in the day a foot soldier could make a bit of money in a battle by knocking a knight off his horse, and then holding him for ransom. The weapon that they used for this was generally known as a poleaxe. These come in various shapes, but one general idea was to have a hammer on one side of the long pole. Thus, by swinging the pole one could hit a knight with a force of say 50 – lbs. and this could knock him off his horse, allowing him – in the best of such worlds – to be captured alive and then ransomed.

Modern Reproduction of a poleaxe

Figure 5. Modern Reproduction of a poleaxe from about the time of the Wars of the Roses (Wallace Collection)

However that hammer head could measure about a square inch or two, and neither the force nor the pressure would have been enough to penetrate armor or a helmet of the type King Richard wore (Figure 1). To give the footman that advantage the design was changed to include a small spike in the center of the hammer.

Spiked Poleaxe

Figure 6. Spiked Poleaxe from about 1582, (Royal Armories, Leeds via My Armory.com)

Now when the force of 50-lb is applied through the hammer to the target it is not distributed over a square inch (giving a pressure of 50-psi). Instead it is focused down on a point that is less than a twentieth of an inch across. Total area of the circular point comes from pi x radius squared = 3.14 x 0.025 x 0.025 = 0.002 sq inches. Pressure applied through the spike to the helmet = 50/0.002 = 25,000 psi. That is enough for the spike to pierce through the metal helmet and the bone underneath, killing Richard III. Battle over, England had a new king, Henry VII, and the War of the Roses was over.

The intent of the two examples is to show how, in some circumstances, high volume flow rates at low pressure can do the most damage, and in others that much higher pressure applied over a much smaller area is the most effective. They are extreme examples but seek to illustrate the point, and in many cases neither extreme (highest pressure, lowest flow or lowest pressure, highest flow) will give the best answer.

Aluminum Cutting

Figure 7. Cutting 6” Aluminum with KMT Waterjet Streamline PRO Pump 60hp 90,000psi.

There are cutting conditions where operational concerns and benefits would argue that pressures of 90,000 psi, and flow rates around 1 gpm will be the best business choice. In other cases a flow of a thousand gpm, but at a pressure of 1,000 psi will be the most economic and viable way to remove soil, and weaker rocks like coal. This series is aimed, in part, at giving you the knowledge that will help you decide where, within that range, to make that balance, between flow and pressure.

Waterjet Weekly Blog-A New KMT Waterjet Series

KMT Waterjet Systems Weekly Waterjet Blog

KMT Waterjet Systems Weekly Waterjet Blog

I have been a Curators’ Professor at the University of Missouri Science and Technology since 1980. For most of my career I have led a team developing the uses of high pressure waterjets, and these have ranged from the removal of skin cancer, and precise material cutting at the millimeter level, up to the carving of statues (including a Stonehenge) some 5 meters high. Waterjet technology has been developed to cut open, disarm, and remove the explosive from munitions, and mines.

In October of 1965 I started work on a doctoral dissertation that would look at whether streams of high-pressure water could be used to mine minerals, rather than using the mechanical tools that my ancestors had been using for many generations to mine coal. Until the time of my great-grandfather the main tool had been a hand-swung pick, but he had made the transition to become a compressed-air-powered, coal-cutter operator, and worked with my grandfather on running that machine until the first World War, when his son joined the Northumberland Fusiliers and went off to Belgium.

When I started my work, after my mining engineer father had approved, I found that there was little information on hydraulic mining available in the technical literature. The Internet did not exist, and the few books and articles that I could obtain came through the Brotherton Library at Leeds University, where Inter-Library Loans would find a source, and even, on occasion, a translation, but in weeks not days.

Those conditions no longer hold true, and yet, while a computer now makes it easier to get instant access to all the world’s knowledge, filtering through that vast stack to find that needed bit of information still takes time. And there are other factors that have come into play, so that much of the knowledge that has been gained may soon be lost, forgotten or spread into so many distant places as to be effectively gone. And so I am going to put together a new series of posts about this technology. Since this is the first it is more of an explanation of the background, and as the posts continue so the structure and location may change, trying to better serve those who follow me in what has been the truly fascinating development of a new very broad-based industry.

Over the past decades high-pressure waterjets have found a wide variety of different uses around the world. From the small pumps that can be bought at the local hardware store and allow you to clean houses, furniture and cars through the thousands of horsepower used in pumps for the excavation and mining/petroleum industry a quiet revolution has occurred in many industries, beyond the sight of the general public. I was fortunate enough to be a part of the relatively small group of scientists/engineers/technicians who helped bring these changes about. Around the world there were perhaps 50 or so of us, and much of our interaction took place at conferences, where we learned more from each other in bars and restaurants than we did from the formal papers that we all gave. Some changes were fairly dramatic, the use of cleaning jets on oil platforms comes to mind, and were instantly adopted, others were a longer struggle, and yet these tools have yet to find more than 90% of their ultimate market, which will likely be in fields that most of us have not even thought of yet. And the tools that have already been developed are used in many more industries than the general public understands.

I retired a couple of years ago, and followed many of that original group in moving on to other interests. Before I left, however, I had written a book, and taught a class to senior undergraduates dealing with manufacturing use, as well as the earlier mining applications. The class is not taught now, and interest in the topic has also shrunk at the other major universities, as faculty have changed, and other topics bring the “research rain” that is needed to sustain the graduate classes of today.

This does not mean that waterjetting is less valuable, but instead is recognizes that the first flush of development is over, and that the really low-hanging fruit of application has been picked by folks such as myself. The range of applications remains immense, but the rewards are not now as easily obvious, and the research results now are not so dramatic.

The current plan is to begin the series with posts that come from my lecture set. But instead of being of the usual length they will be broken down into a set of sub-topics, so that there may be three or four posts that will cover the material of a single class. This will make each post of around a thousand words, and then the four sub-topics will be combined into a “class” version which will be posted as a pdf, and this will be down-loadable, and could be printed and put into what will, over time, become a somewhat updated version of that earlier book, but in a different format.

Since none of the anticipated readership is yet aware that this is happening, I expect that it will take some time for comments and questions to develop, but as these do they will be added into the mix.

Once the original posts have become established I hope to be joined by some of the folk that are still working in the field – as I said earlier it is one that is still continuing to grow at a fairly steady pace (one of the companies that makes equipment was on the national news recently because it could not get enough trained folk to help it meet demand). New ideas will turn up, and I look forward to giving my opinions. Sadly these may appear a bit negative at first, but there were many things we tried that looked good, but did not pan out. And those were usually not, therefore, the things that we wrote papers about. But knowing something won’t work, and more particularly why not, is also useful.

The early posts will also deal more with the history and general background, since these are likely to have a more general interest, and the more technical parts of the discussion will come later, though I will try and keep that at a relatively simple level for explanation.

I got my last patent this week, it dealt with drilling oilwells – the one before that dealt with treating skin cancer. I have worked on intercontinental ballistic missiles, at nuclear facilities, on land-mine clearance and in blocked caves. So perhaps I could claim to be a surgeon, rocket scientist, nuclear scientist, fire-fighting expert, and hazardous material specialist – and that neglects all the work on manufacturing and the evolution of tools that can cut through an inch of material within an accuracy of a thousandth of in inch.

All because of the power that comes when you push a pint of water through a tiny hole. Who’d a thunkit!!