Waterjetting 31a - Changing Jet Pressure, Diameter and Exposure

A high-pressure waterjet will penetrate into a material by penetrating into small cracks in the surface and pressurizing those cracks, so that they grow and join together freeing material. This mechanism changes where one moves to add abrasive, but that discussion will come later.

The larger the cracks in the material, then the lower the pressure needed to penetrate into the crack, and to then cause it to grow. Large grained, weakly bonded material, such as for example soil, can, as a result be washed apart by pressures as low as those caused by a heavy rain. As the material becomes more cohesive (think initially of a heavy clay) then the amount of force required to grow the fissures is greater, while the crack lengths are usually smaller. This means that the jet pressure will have to be higher for the same volume of material to be removed.

As one moves from soils to rocks and other materials will increasingly smaller grain size, so the pressure required to cut into the material must be increased. Initially we call the pressure at which the jet starts to dig a hole the initial pressure or threshold pressure of the material.

The way to find out its value is to point the jet at right angles to the jet and begin to raise the jet pressure. When the jet has not enough pressure to penetrate and grow cracks in the target, then it will flow along the surface after impact. However when the jet starts to drill a hole into the target, then the water going into that hole has only one way out – back the way it came, and now the jet comes back along the axis of the jet. (Hitting the operator if the lance is hand-held and this is partly why you need personal protective equipment).

Generally that pressure is not enough to give an economic removal rate and the jet pressure should be raised significantly above the threshold to reach that level. All other things being equal (such as nozzle diameter, standoff distance and traverse speed) then as the jet pressure is raised the depth of the cut will increase in proportion, as will the volume of material removed. This is the case whether the pump providing the water is an intensifier system (usually at higher pressure) or a triplex or similar pump. The main difference in the plot is because of the difference in the diameter of the cutting jets. Berea sandstone is a “standard” rock that has been used in many cutting tests over the decades because of its relatively uniform structure and strength. The uniaxial compressive strength of the sandstone is around 5,000 psi.

Figure 1. The effect of raising jet pressure on the depth of cut achieved in Berea Sandstone with the cuts made at a speed of 12 inches/minute.

This leads into consideration of the second important parameter, that of the flow rate of the jet, which is mainly defined by the diameter of the orifice through which the jet is formed. The flow volume of water is controlled both by the jet pressure (the higher the pressure the faster the water flows out of the nozzle) and by the diameter of the jet. When one is cutting with water alone then it is often better to have higher flow rates at lower pressure rather than the converse. The reason for this is that larger diameter jets hit more flaws on the surface than smaller ones, and the larger the area that is under attack then the greater the likelihood of larger cracks being present and allowing greater volumes of material to be removed. (There are statistical and mathematical justifications for this, but I will forgo going through that math).

When carrying out rough calculations on relative cutting performance over the years we have assumed that the relationship between the depth of cut and the diameter of the orifice is a power relationship with an exponent of 1.5. When comparing the data for Berea sandstone which we obtained as we changed jet diameters we found the following:

Figure 2. The effect of increasing jet diameter on the depth of cut achieved in Berea Sandstone with the cuts made at a speed of 12 inches/minute.

The exponents are not quite at 1.5, but using that value gives a fairly close initial estimate as to the performance that we can achieve.

Part of the problem in seeking a correlation between the jet cutting performance and the nozzle diameter is that the cutting range of the jet changes quite quickly with a change in nozzle diameter. And while we often use a first rough estimate that the jet throw is 125 – 150 diameters in reality the jet performance changes over that range, as the structure of the jet itself changes.

One way of showing this is to show how the cut depth varies when the target surface is at different distances from the nozzle, a value we often call the stand-off distance. In this case the rock is a sandstone, and similar to that used above, but the tests are made with the jet firing at the rock for different lengths of time, rather than traversing over it.

Figure 3. The effect of increasing exposure time and standoff distance on the depth of hole achieved in Sandstone.

Note that there is a relatively rapid drop in cutting performance as the target is moved away from the nozzle, which had a diameter of around 1 mm (0.04 inches). But the plot also shows that the cutting depth drops away very rapidly with time. After half-a-second the jet has cut roughly half an inch deep when the target is half an inch (12.5 mm) from the nozzle, but after doubling the exposure to a second the jet has only increased the depth of cut to 0.6 inches (15 mm) and with the time of exposure increased to five seconds the depth only increases to around 0.7 inches (17.5 mm).

This will be the topic for the next post, where the effect on the speed of cutting is the subject.

Waterjetting 27c - Drilling nozzle design

In discussing how stress affects the ability of waterjets to drill rock, I have discussed the effect of the stress in the ground on drill performance, but before discussing the effect of the borehole pressure it is perhaps best to spend this post talking about the simplest drill bit design.

The diameter of the first jets we used to cut into rock were about 0.04 inches in size, with the nozzle holder used to hold the nozzle on the end of the supply pipe being at around an inch in diameter. As a result, if the jet was to cut a path into the rock, it would have to rotate around the face of the rock ahead of it, removing all the rock ahead of the assembly, and allowing the head to advance.

Figure 1. Original concept of a waterjet drill used to penetrate sandstone.

Of course, back when we first did this in the 1960’s the swivels weren’t available to allow us to rotate the high pressure line, and so we rotated the rock samples instead.

Figure 2. First holes drilled at the University of Leeds. Note the central cone.

Because the jet had to penetrate across the diameter of the hole, so as to remove the cone ahead of the tool, and since the jet would only cut around 2.5 times the jet diameter in width at any one time, the rate that the head could move forward was limited to a maximum of 0.1 x rotation speed (rpm) in inches/minute. And, because the rotation speed controlled the depth which the jet cut into the rock, the rpm had to be kept down to ensure that the jet cut to the full required diameter on each pass. The top speed we could achieve, even in relatively soft sandstone, was around 4 inches a minute.

One of those fortunate accidents that sometimes befalls research folk then occurred. I had asked Jim Blaine, our machinist, to make a new design, with one jet pointing forward and one off to the side, intending that the two be offset. However, due to a misunderstanding, he drilled the second, smaller hole along the jet axis, while offsetting the angled jet to cut further out from the diameter. Since the nozzle was built we proceeded to try it.

Figure 3. First dual jet nozzle design.

Because the axial jet removed the central core, we could offset the inclined jet so that it needed to cut a shorter distance in order to reach the required gage for the hole. That meant that we could rotate the nozzle faster, which in turn meant a faster drilling speed, much faster.

Figure 4. Hole diameter as a function of rate of penetration of the drill (in meters/minute), for two outer jet angles, and two rotation speeds.

Note that in the above figure, with a 30 degree outer jet, spinning at 970 rpm we were able to drill a hole at a speed of roughly 280 inches/minute instead of the previous 4 inches/min by adding only 25% more water to the bit with the second orifice.

As mentioned above, the limit on the advance rate was the depth which the jet cut into the wall, and the amount of rib between adjacent passes that the jet cut would leave.

Figure 5. An early hole drilled into Berea sandstone, at a slow advance rate, using a 10 ksi jet pressure.

Figure 6. Hole drilled into Berea sandstone at 970 rpm, 225 ipm advance rate, with a 15-degree inclined jet. Note that the hole perimeter has the equivalent of a thread cut into it.

It is pertinent to make a small observation over the advantage of that slightly roughened outer wall to the borehole. One of the ways in which miners hold up the roof while they are working underground, is to insert rods (known as roofbolts or rockbolts) into drilled holes placed in the surrounding rock. To improve the grip between these bolts and the wall, miners will also often insert packages of glue into the hole to fill the gap between the bolts and the rock wall.

Unfortunately when the hole is drilled with a conventional mechanical drilling bit, the walls of the hole are left relatively smooth. This means that the bolt has a poorer grip on the wall, and is more easily pulled out of the hole. The US Bureau of Mines ran anchorage tests for different rock wall finishes.

Figure 7. Effect of hole roughness on the anchor strength (US Bureau of Mines)

Conventionally a larger hole, with greater bearing surface, would give a stronger anchorage. This is shown by the greater load carried by the hole drilled with the 1-3/8th bit, over that drilled by the 1-1/4 inch bit. But both of these were smooth walled, and the bit drilled at 1-inch, with a roughened wall had almost three-times the pull strength even though of smaller size.

The roughness of the hole can be controlled by adjusting the feed rate, relative to the rotation speed, both as a function of the jet pressure, nozzle diameter and outer jet angle. It turned out, through experiment, that the optimal angle for the jet was at around 22.5-degrees, depending on the type of rock in which the drill was working.

The effect of rock properties plays a very significant role in the performance of the drill. And it was very easy, early in the program, to show that the important rock parameter was not the compressive strength of the material. To show this we drilled through prepared samples of an Indiana limestone and a sandstone, both of which had approximately the same (uniaxial) compressive strength. The advance rate was kept constant, as was the rotation speed, as the drill penetrated from one rock into the other, and then the hole was cut in half (as were the samples shown above).

Figure 8. Hole drilled from limestone into sandstone.

Although the hole maintained alignment, drilling straight forward through the steep interface between the two rocks (a problem with some conventional drills) the hole diameter changed dramatically.

How we changed the design to maintain hole diameter, and, at the same time, adjusted for changing borehole depth will be discussed next time.

Waterjetting Technology - 26a More on waterjet assisted cutting

When mankind first began cutting out flints to make the tools and weapons that helped make primitive life more successful they often used either bone antlers or stones from the river as the tool to cut into the chalk or other host rock that held the flint. For thousands of years as rock was excavated for broader use, including making building stone, the rock continued to be cut manually, and it has only really been in the last hundred and fifty years that manual picks have been replaced with power driven machines. However, in great part, the machines have had to be made larger and heavier than they might need to be because, in large part, unlike the pick swung by a miner, the machine cannot selectively attack the rock that it is facing, but must cut along a foreordained path.

Figure 1. Conventional tool path in cutting concrete, the tool has to cut through both the hard aggregate pieces as well as the softer cement.

The tools that cut through the rock mechanically must, therefore, be able to cut through all the different materials that they are likely to encounter. Where the rock is like a concrete, with hard and soft parts, then the tool must be able to cut through the hard (aggregate) as easily and fast as it removes the soft (cement) phase if the machine is to maintain productivity. When I wrote about cutting concrete, I pointed out that this “brute force and ignorance” approach to getting through material was expensive in the time that it took to make a hole, and in the energy that had to be expended, both combining to make the overall process itself more expensive than it need be. That cost includes not just the costs of the process itself, but is also less obvious in that the machine itself has not only to be bigger, but because it also typically sees a wide range in force applied through the cutters to the drive mechanism, it also has a shorter operational life because of these fluctuations. (One shearer model saw such failures within six months of start-up).

There are a number of different ways in which the sensible application of high-pressure waterjets can improve cutting performance, lower machine size and cost and provide a win-win situation. But there is a need for caution, since the small size of the waterjets that are often used is much below the scale of many other parts of the machine, and, as a result, the precision with which the jets need to be applied can often be neglected.

In an earlier post on this topic, I discussed how a mechanical tool will crush the rock over which it passes during cutting. This crushed rock confines the bit, and is often re-compacted so that frictional forces rise, and the temperatures can be high enough to soften tungsten carbide.

Figure 2. Crushed rock under the impact of a mechanical pick. The size of the indentation relative to the size of the crushed rock is evident.

If the jet is to be effective it has to be directed into the cut at the point where the crushed rock is being created, so that the jet can remove the broken pieces as they are being formed. It is this critical location of the jet relative to the bit:rock contact that is often missed by those who have tried to apply this technology in the years since Dr. Mike Hood first demonstrated the benefit.

A number of experiments over the years showed that if the jet is more than about a tenth-of-an-inch (2.5 mm) from the point of the pick where it enters the rock (or the edge of the tool if it is a broader shape) then the jet will not be able to reach and remove the crushed material. This is particularly true when the rock being cut is, as in the above figure, a basalt, which the jet of water cannot normally penetrate at pressures of 10,000 psi. thus, if the jet does not reach the crushed material then the energy put into its creation has been wasted.

There are two parts to that last statement. They deal with all three planes in which the jet lies, relative to the point of pick contact. There is the relative position at which the jet hits the rock, where it is critical that it hits just where the rock is being crushed, and then there is the distance of the nozzle from that contact point. The latter point is one that I have also written about in earlier posts, but which can also be neglected when engineers are designing systems. There are a number of papers (which seemed to be at a peak at the 8th International Waterjet Symposium in Durham, UK in 1986) where this distance was set incorrectly (values up to 0.3 inches and above were reported) and it is not, therefore, surprising that some investigators found that the results were not as good as expected.

Figure 3. Jet cutting at the front edge of a pick (Front cover of the 8th International Symposium on Jet Cutting Technology, BHRA, Durham, UK, Sept. 1986)

If the nozzle is too far from the rock contact, then the pressure of the jet will have fallen to a pressure that is too low to be effective. This has been a less obvious problem to overcome, since to many observers the jet seems coherent with distance, but, given that jet flow is often divided between a number of different nozzles on the cutting head, the individual orifice sizes can be quite small (perhaps 0.01 inches in diameter). If the effective jet throw distance is 125 diameters, then the range of the jet is 1.25 inches. Yet in a number of applications, because of difficulties in fitting the nozzle in place, the orifice can be placed more than 2.5 inches from the rock contact. Again the result of this is to make the jet sensibly ineffective.

The jet has to be put into the right place, and with the correct amount of power, if it is to be of any use. Sometimes that can mean that the nozzle is placed behind the pick (so that it can be protected by the pick from the rock, yet can be brought close enough to the crushed zone that it can penetrate it from behind. This is a little more difficult to achieve, since the precision of location is a little more difficult.

Others have tried feeding the jet down through the pick, and I will explain some of the benefits and problems with this as I continue on this theme next time.

Waterjetting 18a - air and abrasive

As high-pressure waterjet systems have continued to expand into broader fields of application, that increased range has been significantly expanded where abrasive has been added to the jet stream. Abrasive waterjets are more widely used in cutting those materials that are less easy or practically impossible to cut cleanly with water alone (although that is a relative statement, since metal, for example, can be cut at higher water pressure without abrasive).

But before there was high-pressure abrasive waterjet cutting there was sand blasting and other applications of abrasives existed in cutting and material removal – think, for example, of sandpaper. The first “powered” use of sand to remove material has been credited to B.C. Tilghman Jr. of Philadelphia whose British Patent was number 2,147, an indication of how long ago it was. (His American patent was number 104,408). In his review of the topic in 1972 Plaster noted that the patent was fairly comprehensive in regard to some later developments. It in included a system wherein the abrasive was carried by means of

a jet of steam, air water and other suitable gaseous or liquid medium . . . . .the sand may be propelled by a current of air produced by suction or a partial vacuum. . . . . . When a jet of water under heavy pressure is used, as in hydraulic mining, the addition of sand will cause it to cut away hard and close grained substances, upon which water alone would have little or no effect.

Figure 1. Illustration of the initial steam-injected sand blasting design (after Plaster)

At the time that the invention was made steam was the easiest fluid to provide the driving pressures and volumes needed to power the abrasive stream.

The original machine was operated by steam at a pressure of up to 400 psi, and sand was fed from a feed funnel, down through a length of hose into a narrow (0.17 inch diameter) tube centered within the half-inch diameter steam tube. This tube tapered down to a quarter-inch inner diameter as it reached the end of the sand feed line, leaving a narrow gap around the exit to the sand pipe. The high velocity of the steam, as it then flowed the chamber at the end of the sand pipe created the vacuum that pulled the sand into the stream. The resulting jet was collimated by a 6-inch piece of quarter-inch pipe.

It was found, experimentally, that putting a pair of aligned, 3-inch long flat plates on the end of the nozzle, aligned with its edges, gave a better jet, with less lateral spreading when grooves or straight cuts were required.

Steam, however, wet the sand, which would then attach itself to the pipes, causing blockages. Problems also arose because the steam caused poor visibility, and made for unpleasantly hot and wet working conditions. Thus there was an incentive to change, and by the turn of the century (1900) the increasing popularity of compressed air provided an impetus for this change and compressed air then became the main fluid transport for the abrasive throughout the 20th Century. By 1984 production rates for such systems of around 4 sq ft/minute could be achieved by a single operator working with a system driven by a 12 hp. compressor.

As the technology became more widespread so the design of the nozzle was improved through a series of modifications. These led to the inclusion of what is known as a de Laval nozzle into the design of the delivery system. The de Laval design was initially used to drive a small steam turbine in a creamery in 1897, by Gustaf de Laval.

Those who first sought to make steam turbines were also the first to have a large steady supply of an elastic medium that is very like a gas, steam. They soon found themselves using nozzles to produce high-speed flow and they started by using convergent nozzles and they mostly still do. This was the intuitive design with its forerunner in use in hydraulic machinery. They soon found that whilst they could increase the speed of the jet formed by a given convergent nozzle by increasing the supply pressure, no comparable increase could be produced by reducing the back-pressure. They described the nozzles as “choked”. It must have been totally counter-intuitive to find that the fitting of a divergent cone to a convergent nozzle got rid of the problem.

In its simplest form the nozzle takes the form of a convergent section, followed by a narrow constant diameter throat, and this is succeeded by a diverging section at the end of the nozzle.

Figure 2. Basic components of a venture nozzle for abrasive blasting with air.

The increasing diameter of the channel, after the throat, causes a drop in pressure in the nozzle. This, in turn, allows the air to accelerate with the abrasive and the velocity resulting is more than twice as high as it otherwise might reach, going from perhaps According to tests by Tetrabore in 1981, velocity changes from 275 ft/sec to 650 ft/sec have been measured. At the same time the improved velocity of the jet made it effective over a greater area of the target with effective cleaning reported as increasing by 30 - 40%.

A specific design was patented by Albert in 1955, where the transition lines are radiused rather than being linear.

Figure 3. Based on the nozzle design patented by Albert (Plaster ibid).

There are two other advantages to the design beyond the improved air velocity as it leaves the nozzle. The first of these is that the flow is more uniform coming out of the nozzle, so that the surface being cleaned is more evenly attacked, reducing the need for nozzle manipulation to ensure that the surface is completely covered during cleaning, and secondly the amount of abrasive that is required to clean a given surface might be reduced by as much as 20%.

It is in this control of the air component of abrasive blast streams that there thus remains some potential for further improvement. But we will discuss that and other aspects of abrasive use in the following parts of this section.

Waterjetting 7a - An intro to jet structure

Once a waterjet starts to move out of the nozzle with any significant speed, as the pump pressure begins to build, it becomes more and more difficult to look at the stream of water and get any realistic idea of its structure. Mainly what is seen is the very fine mist that surrounds the main body of the jet, and while some idea of the structure can be obtained by making cuts through material, it can be quite expensive to actually see within that structure. Part of the problem is that though the mist is very fine, it is also moving at speeds in the range of a couple of thousand feet per second. The human eyeball isn’t quite that fast. But we can use a very high-speed flash (in this case it was on for two millionths of a second) which has the effect of “freezing” the motion.


Figure 1. 40,000 psi jet issuing from a 0.005 inch diameter orifice, front lit.

However this mist still hides the solid internal structure of the jet and does not change much in relative structure, even when the internal jet conditions can be quite different. Fundamentally the internal structure was described by Yanaida at the 1974 BHR Group Waterjet Conference, and his description has been validated by many studies since.


Figure 2. The break-up pattern of a waterjet (Yanaida K. “Flow Characteristics of Waterjets,” 2nd BHRA Conf. 1974, paper A2.)

This structure holds for jets across a wide range of pressure and flow volumes, but it is difficult to determine the exact transition points of that structure conventionally. And this can lead to very unfortunate results. I have twice seen people back a nozzle away and then move their hand in front of the jet to show that even high-pressure jets (these were being used to cut paper products and had no abrasive in them at the time) could be “safe.” If both cases the individuals were very lucky to escape injury (water can penetrate the pores of the skin and lacerate the internal parts without any surficial signs of injury, and, as I showed last time, if the nozzle is too close it will slice through flesh and bone). I thought to take today’s post to show, though the use of photographs, why that was such a stupid action.

The photos were taken down at Baxter Springs, KS in the early 1970’s and involved the use of what was then a MacCartney Manufacturing Co intensifier, to shoot jets of varying pressure, and nozzle diameter along a path, so that we could see how coherent the jets were. As I mentioned above, the problem with looking directly at the jet is that the internal structure is hidden by the surrounding mist. To overcome that part of the problem we shone the light along a ground glass screen (to diffuse it) that was placed behind the jet, so that we could see the outline of the internal structure.


Figure 3. Arrangement for taking photographs of a high-speed jet.

This more of the downstream mist from the photograph, and a much better idea of the internal structure of the jet, and where the solid section ended could be measured.


Figure 4. Backlit, 30,000 psi jet issuing from a 0.01 inch diameter nozzle, the distance across the photograph is 6 inches.

The benefit of the technique is perhaps more evident when nozzles at different pressures and diameters and different chemistry are compared. First consider the change with an increase in jet diameter. From the front-lit view there is little difference in the jets. From the backlit, it is clear that the smaller diameter jet only reaches 3-inches across the screen, while the larger jet barely reaches the end of the range.


Figure 5. The effect of doubling the orifice diameter at the same jet pressure on jet range, the photo length is 6 inches.

One of the parts of the study we were carrying out in 1974 was to examine the effect that adding different long-chain polymers had on jet structure. The ones that we were looking at include some that are now used in the oil and natural gas industry to make the “slick water” that is used in the fracking industry to improve production from shale reservoirs. But it also has an advantage in “binding” the jet together. And so, in the study, Dr. Jack Zakin and I tested a wide range of different polymers to see which would be give the best jet.

There were a number of different things we were looking for. In cutting paper, soft tissue and water sensitive material for example, the polymer can bind the water sufficiently well as to further lower wetting to the point where it doesn’t have an effect. It also can improve jet cutting under water – but I’ll cover those in a few post on polymer effects that will come to later in the series.

The effect of a polymer (in this case an AP273) is shown in two tests where the only change was to add the polymer to the water for the lower one.


Figure 6. Jets with an orifice diameter of 0.01 inches at a pressure of 20,000 psi, the range is 6 inches, and the lower jet has had the polymer AP273 added to the water.

The narrower stream in the lower frame is the effect that we were looking for. Putting change in diameter and the better polymers together gave, as an example, the following:


Figure 7. The effect of changing jet pressure, nozzle diameter and polymer content on jet cohesion.

It might be noted that the jet in the bottom frame has as much relative concentration (and power) at the end of the range as the top jet had at the beginning of the range.

Now it all depends on what you want the jet to do, as to which condition you wish to achieve. Inside abrasive mixing chambers the object is much different than it is when the object is to cut a foot or more of foam with high quality edges. And there have been some interesting developments with different polymers over the years, but I’ll save those stories for another day.

But bear in mind that those individuals who could slide their fingers under the jet in the top frame of figure 7 would have had them all cut off if the jet had been running instead under the conditions of the bottom two frames, and in all three cases, to the naked eye the jets looked the same.

Waterjetting 3d - High-pressure pump flow and pressure

When I first began experimenting with a waterjet system back in 1965 I used a pump that could barely produce 10,000 psi. This limited the range of materials that we could cut (this was before the days when abrasive particles were added to the jet stream) and so it was with some anticipation that we received a new pump, after my move to Missouri in 1968. The new, 60-hp pump came with a high-pressure end that delivered 3.3 gpm at 30,000 psi. which meant that a 0.027 inch diameter orifice in the nozzle was needed to achieve full operating pressure.

However I could also obtain (and this is now a feature of a number of pumps from different suppliers) a second high-pressure end for the pump. By unbolting the first, and attaching the second, I could alter the plunger and cylinder diameters so that, for the same drive and motor rpm, the pump would now deliver some 10 gpm at a flow rate of 10 gpm. This flow, at the lower pressure, could be used to feed four nozzles, each with a 0.029 inch diameter.

Figure 1. Delivery options from the same drive train with two different high-pressure ends.

The pressure range that this provided covers much of the range that was then available for high-pressure pumping units using the conventional multi-piston connection through a crankshaft to a single drive motor. Above that pressure it was necessary to use an intensifier system, which I will cover in later posts.

However there were a couple of snags in using this system to explore the cutting capabilities of waterjet streams in a variety of targets. The first of these was when the larger flow system was attached to the unit. In order to compare “apples with apples” at different pressures some of the tests were carried out with the same nozzle orifice. But the pump drive motor was a fixed speed unit which produced the same 10 gpm volume flow out of the delivery manifold regardless of delivery pressure (within the design limits). Because the single small nozzle would only handle a quarter of this flow, at that pressure (see table from Waterjetting 1c) the rest of the water leaving the manifold needed an alternate path.

Figure 2. Positive displacement pump with a bypass circuit.

This was provided through a bypass circuit (Figure 2) so that, as the water left the high-pressure manifold it passed through a “T” connection, with the perpendicular channel to the main flow carrying the water back to the original water tank. A flow control valve on this secondary circuit would control the orifice size the water had to pass through to get back to the water tank, thereby adjusting the flow down the main line to the nozzle, and concurrently controlling the pressure at which the water was driven.

Thus, when a small nozzle was attached to the cutting lance most of the flow would pass through the bypass channel. While this “works” when the pump is being used as a research tool, it is a very inefficient way of operating the pump. Bear in mind that the pump is being run at full pressure and flow delivery, but only 25% of the flow is being sent to the cutting system. This means that you are wasting 75% of the power of the system. There are a couple of other disadvantages that I will discuss later in more detail, but the first is that the passage through the valve will heat the water a little. Keep recirculating the water over time and the overall temperature will rise to levels that can be of concern (it melted a couple of fittings on one occasion). The other is that if you are using a chemical treatment in the water then the recirculation can quite rapidly affect the results, usually negatively.

It would be better if the power of the pump were fully used in delivering the water flow rate required for the cutting conditions under which the pump was being used. With a fixed size of pistons and cylinders this can be achieved, to an extent, by changing the rotation speed of the drive shaft. This can, in turn, be controlled through use of a suitable gearbox between the drive motor and the main shaft of the pump. As the speed of the motor increases, so the flow rate also rises. For a fixed nozzle size this means that the pressure will also rise. And the circuit must therefore contain a safety valve (or two) that will open at a designated pressure to stop the forces on the pump components from rising too high.

Figure 3. Output flows from a triplex (3-piston) pump in gpm, for varying piston size and pump rotation speed. Note that the maximum operating pressure declines as flow increases, to maintain a safe operating force on the crankshaft.

The most efficient way of removing different target materials varies with the nature of that material. But it should not be a surprise that neither a flow rate of 10 gpm at 10,000 psi, nor a flow rate of 3.3 gpm at 30,000 psi gave the most efficient cutting for most of the rock that we cut in those early experiments.

To illustrate this with a simple example: consider the case where the pump was used configured to produce 3.3 gpm at pressures up to 30,000 psi. At a nozzle diameter of 0.025 inches the pump registered a pressure of 30,000 psi for full flow through the nozzle. At a nozzle diameter of 0.03 inches the pump registered a pressure of 20,000 psi at full flow, and at a nozzle diameter of 0.04 inches the pressure of the pump was 8,000 psi. (The numbers don’t quite match the table because of water compression above 15,000 psi). Each of these jets was then used to cut a slot across a block of rock, cutting at the same traverse speed (the relative speed of the nozzle over the surface), and at the same distance between the nozzle and the rock. The depth of the cut was then averaged over the cut length.

Figure 4. Depth of cut into sandstone, as a function of nozzle diameter and jet pressure.

If the success of the jet cut is measured by the depth of the cut achieved, then the plot shows that the optimal cutting condition would likely be achieved with a nozzle diameter of around 0.032 inches, with a jet pressure of around 15,000 psi.

This cut is not made at the highest jet pressure achievable, nor is it at the largest diameter of the flow tested. Rather it is at some point in between, and it is this understanding, and the ability to manipulate the pressures and flow rates of the waterjets produced from the pump that makes it more practical to optimize pump performance through the proper selection of gearing, than it was when I got that early pump.

This does not hold true just for using a plain waterjet to cut into rock, but it has ramifications in other ways of using both plain and abrasive-laden waterjets, and so we will return to the topic as this series continues.

Waterjetting 1c - Volume flow, horsepower and thrust tables

Over the course of my career there is one table that I have used, for one reason or another, just about every week. Most folk will not likely need it nearly that often, but it contains some information that can be handy, if it is suddenly needed.

The table provides the relationship between the pressure of a waterjet system, the size of the nozzle that the water is fed through, and the resulting flow rate that is being used, the horsepower of the jet, and the thrust that the jet will exert back on the equipment/person holding the nozzle.

It is a very straightforward set of calculations, and I will build the table in two parts. The first will be a line-by-line explanation of how the calculations are made, and what the basis is, and then I will provide a tabular format (which is the one that I use) from which values can be read off. Because this is built in Excel the values on the edges of the table are changeable, to fit your own particular set of needs. Construction of the tables will be given through a series of 30 steps.

I am going to write about the parts that make up a system to deliver water under pressure in later articles, and so some things that will be explained then are going to be just stated at this point. The first of these comes when one considers nozzle size.

A nozzle, at its most basic, is a hole of a fixed size. Under just the force of gravity flow is quite low, and to get more water to flow through that hole some pressure must be applied to the water. The very simple relationship between the pressure at which the water is pushed, and the resulting speed of the water is given by the equation:

Speed (ft/sec) = 12.5 x square root of pressure (in psi)

Please note that water starts to compress significantly at about 15,000 psi. For the sake of this initial set of tabulations I am going to neglect that issue, though it will come up at some future date.

1. Since pressure is a value that is often chosen by the operator, the value for pressure is entered into cell c3. For this example, a value of 10,000 is used. (These come from the first system that I worked with, back in Leeds in 1965).

2. The equation to determine the velocity of the water is entered into cell c4 as

[ =12.5*sqrt(c3)].

Because the units need to be consistent going through the calculation, inches will be used initially. So the initial velocity value is multiplied by 12.

3. To convert into inches/second, the value in cell c4 is multiplied by 12 in cell c5 using the equation:

[ = 12*c4]

4. Nozzle diameter is the exit diameter of the nozzle, and this is sometimes referred to as the orifice diameter. This is a selected value and is entered into cell c6. I am using 0.04 inches in the initial example.

The cross-sectional area of the orifice is given by the equation:

Cross-sectional area = π x (radius) squared

5. Orifice cross-sectional area is calculated in cell c7, by entering the equation:

[ = 3.1412*((c6/2)^2)]

As water flows through a hole, the stream does not flow out of the hole at the same diameter as the hole. As the flow enters the hole it necks down to a slightly smaller diameter, which is a function of the nozzle shape, among other things. The reduction is known as the Coefficient of Discharge for the nozzle, and is a specific value for an individual orifice that can vary from a value as low as 0.61 to a high of around 0.95 or better. This is an input value, based usually on a manufacturer’s statement.

6. Enter a coefficient of discharge value, I have used a value of 0.81, in cell c8.

7. Calculate the effective area of flow by entering the equation into cell c9.

[ = c7*c8]

By multiplying the area of the flow by the velocity (the length of the water column that flows through the orifice in a second) then the volume of water that flows through the orifice in a second is calculated.

7. Calculate the volume flow each second, by entering the following into cell c10:

[ = c9*c5]

The volume flow rate is normally required in gallons/minute, and the conversion is to multiply by 60 (to convert from seconds to a minute) and then dividing by 231 (the number of cubic inches in a gallon).

8. The calculation is made in cell c11.

[ = c10*60/231]

Computers calculate to a high number of decimal values, and to keep this in normal perspective I usually trim this to show either one or two decimal points. The value shown should therefore be 3.97 gallons/minute, and the table to date should look like this:

Figure 1. The basic steps in calculating the volume flow of water through a nozzle.

There are two other values that are useful to calculate. The first is the horsepower that is being used in the jet. This calculation is a straightforward multiplication of the pressure of the jet (in psi) and the flow rate (in gpm) divided by 1714.

9. Enter into cell c14 the equation:

[=c11*c3/1714]

The other equation that is often useful to calculate (particularly where lances are being held-held in cleaning operations) is the reaction thrust that comes back from the nozzle. Some years ago we validated in the laboratory that this value can be calculated from the equation:

Thrust = 0.052 x flow (gpm) x square root of pressure (psi)

10. Enter into cell c 16 the equation:

[ =0.052*c11*sqrt(c3)]

This gives the basic form for the calculation of the basic values that are most useful.

Figure 2. The initial individual values calculated for the flow.

(You might want to SAVE at this point).

However most of the time I want to do some comparisons and so instead of carrying out a single calculation I would like to see the values in a table.

To make the table I use the same basic equations that are given in the steps above, but I lay out a table of values for pressure and nozzle diameter, which I will step through for those who are less familiar with some of the features of Excel.

The first step is to enter the values that are going to be most useful. In a general table this starts with the pressure that might be used to clean the siding of a house.

11. Insert pressure values starting with 1,500 psi in cell b23, and continuing along the row to that which is used for some of the more intricate cutting of metal, at 90,000 psi, which is in cell L23.

12. The discharge coefficient value is set just above the table in cell c21. I am using a value of 0.81. since this is a common value to all calculations in this table, it is put in a place where it is easy to find and change where needed.

13. Nozzle diameter values are also input as a column down from A24 to A35. I have used values from 0.005 inches to 0.1 inches to cover the range of likely interest, though these can be changed, after all the tables are in place. (Those following along might use the values I provide to create the table, after which use your own values for pressure and nozzle diameter, and don’t forget to change the coefficient of discharge.)

The result, at this point should look like this:

Table 3. Basic structure of the flow calculation table

14. Now, in cell b24 (or the relevant cell in your table) enter the following equation, which combines all the different stages outlined above into one single step.

(=$C$21*(3.1412*60*(A24/2)^2*12*12.5*SQRT($B$23))/231)

The $ sign means that the location after the sign is a constant. It can be selected by highlighting the location in the equation (c21) and then pressing the command and T keys at the same time.

15. Now select the column of values that run from b24 to l24, and then use the Fill Right command under the Edit command in the menu. This will give a series of numbers in the shaded squared that can be ignored for the minute, since we are now going to go through and change some of the values.

16. Go to c24 and change the B24 to A24. Change the $B$23 to $C$23. Tab to D24 and repeat (i.e. change the C24 to A24 and $B$23 to $D$23), and continue doing this along the row, ending in cell L24 changing the K24 to L24, and $B$23 to $L$23). (This is just correcting the calculation to using the right nozzle diameter, and the right pressure values). The table should now look like this:

Table 4. The flow table with the first row completed.

And now take advantage of the power of the table.

17. Select the cells from B24 to L35, and then go to Edit -> Fill Down. The table should be filled in. (You might want to SAVE at this point).

Table 5. Full flow table.

The next step is to create the table for the fluid horsepower contained in the jet.

Because all the calculations tie back to one another from now forward, I am going to use a copy function for the pressure and nozzle diameter values, so that if these values are changed in the above table, they will also change in the dependant tables which follow.

The first step then is to insert the pressure and nozzle diameter values.

18. Go to cell A40 and enter

[=A23)

19. Select row 40 cells A40 through L40. Use the EDIT -> Fill Right command to copy the pressure values into the new table.

20. Select column A cells A41 through A52. Use the EDIT -> Fill Down command to copy the nozzle diameter values into the new table.

21. In cell B41 enter the equation: [=B23*B24/1714] select the B23 and press command T which will change the equation to: [=$B$23*A24/1714)

22. Select the B row from B41 to B52 and use the EDIT -> Fill Down command to generate the first column.

23. Go back to the values in cell B41 and remove the $$ signs from $B$23, hit return and remove the $$ signs from $B$23 in cell B42. Continue down the column removing $$ signs from the cells. The numbers in the cells should not change as you go down.

24. Select the cells from B41 to L52. Enter EDIT -> Fill Right. The second table will generate. While the cells are still selected reduce the number of decimal places to 2. SAVE the file. You have just generated the fluid horsepower table, which should look like this.

Figure 6. Fluid horsepower table.

We will now use the same technique to calculate reaction force.

25. In cell A57 enter [=A23]

26. Select cells A57 to L57. Enter EDIT -> Fill Right, to enter the pressure values at the top of the table.

27. Select cells A57 to A52. Enter EDIT -> Fill Down, to enter the nozzle values along the left-hand side of the table.

28. In cell B58 enter the equation for reaction force in terms of pressure and flow.

[=0.052*B24*sqrt(B23)]

29. Select the cells B58 to L58 and enter EDIT - > Fill Right.

30. Enter cell B58 and select the term B23. Press the command key and T at the same time, which will change this from B23 to $B$23. Tab and repeat this for the C23 term in cell C58, for the D23 term in cell D58 and so across the row ending with changing L23 in cell L58 to $L$58.

31. Select cells B58 to L69. Enter EDIT -> Fill Down. The table should be complete. It should look like this:

Table 7. Reaction Force calculation table.

Congratulations, you now have your own table, and by changing the pressure, nozzle diameter and discharge coefficient values along the flow volume table the charts can be tailored for your own conditions.