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Hy everyone, new here, I don't know much about how high pressure water pumping works - ( i'm just a programmer ) but i need to know if we can create water pressures above 100 000 psi for a crazy water-jet cutting project i have in mind :)

What's the maximum pressure we can reach inside a single pump / or by connecting pumps in series or parallel?

I would like to go to pressures of 500 000 psi or even higher if possible. I have no practical intuition of what that actually means :)

But i know that the higher the pressure the better - my reasoning is - if it takes 5 minutes to cut a big thick block of iron at 100 000 psi- will take 1 minute with 5 times that pressure - ( assume that the other parameters will be scaling as well.)

Taken from here:

At pressures of 60,000 PSI (4,100 bar) and higher, metal fatigue becomes a serious issue with many components. Although pumps that can reach 100,000 PSI have been around for many years, nobody runs them at such pressures because of the extreme maintenance issues involved. For this reason, most manufacturers purposely limit their pumps to below 60,000 PSI (4,100 bar).

This sounds serious - but i'm not too concerned about efficiency here.

I'm interested to know more about the theoretical limits that exist with creating such pressures.. not so much if a pump doing this is available or not for commercial purposes.

What i have in mind is suppose to be a very serious industrial machinery - custom build - all it matters is to cut as fast as possible. All the other concerns like cost or metal-fatigue are secondary.

And also can you please help me picture how big the dimensions of this pump / system of pumps will actually be? What volume it needs to take?

Thanks so much :) Have a nice day!

EDIT 1:

Form @alephzero and @Solar Mike comments (thank you both) i realized there is an important difference between the pressure and the flow rate. This is an xy question and my question title is bad.. sorry about that.

The bottom line is - i need this machine to cut faster - as faster as it can get. I don't think we reached the limits of what's possible with our water jet cutting technologies - and if we did, i want to understand why?

enter image description here

So what are the parameters we need to change - for this cut to happen 5 times faster? Or 10 times faster - or whatever i pick. When we will reach the maximum theoretical and then the practical limit of that this pumps can do.

It will help if we put pumps in series or parallel? It will help if we increase the pressure? Or the flow rate? (but how to increase the flow rate - if the diameter is fixed)

I thought that by increasing the pressure we can make the cut faster. @Solar Mike comment made me realize that i don't need pressure - i need a 5 times higher flow rate - in order to cut 5 times faster. But because the orifice is a certain diameter - i think we can't do it without increasing the pressure.(maybe i'm wrong about this.)

And for now don't worry about how the sand will be mixed with this higher speed jet. Based on this video it seems you can't mix sand if the water jet is at higher speed/ orifice is smaller - but i think i can get around that by combining more water jets into a single one inside a diamond chamber, like this:

enter image description here Not sure if this schematic will mess up the jet shape - but anyway the first problem is to figure out how to get that jet moving faster. Then we worry about how to add sand to it.

EDIT 2:

Based on @Mark answer (thank you) i understand now that is not even possible to build such a pump - because the the maximum pressure we can possibly have is 150 000 psi - if that pump is made out of titanium.

There is no material stronger than that - except diamond, graphene and such - which are not an option. (I found a company that makes nozzles out of pure diamond, specially designed for water-jet cutting - but they don't make any pumps :)) - and for sure what @alephzero said about diamond strengths depends on the angle that force acts on it - applies here. )

Just to keep things simple let's stay with 100 000 psi for now. (such a bummer ..)

I still want to cut faster. What can i do?

If cutting faster is related to flow rate - then i need to increase flow rate somehow.

It follows that the only way to do that - is to increase the orifice diameter. (the other way - is to increase the pressure - which is not an option)

If i double the diameter - and increase the power appropriately - that will quadruple the flow rate.

Now because the diameter is double - the water-jet cross section has quadrupled - the amount of material i need to cut out has quadrupled also - the same as with flow rate. (not 100% sure about this - but is my first intuition)

What i'm trying to understand now is: So what will happen to cutting speed by increasing the diameter - is this a zero-sum game ??

I mean, trying to increase speed -> i increase the flow rate -> by increasing the diameter -> which which increases the jet cross section-> which then increases the amount of material i need to cut -> which lowers the cutting speed all over again. So i go nowhere with this?

Or can be beneficial to increase the diameter? My intuition can't confirm anything here- i need someone to help me understand what will happen in the case i increase the diameter.

Is there a way to get out positive form this situation? Or is a hard theoretical limit like the one with pressure?

I rely don't like increasing the diameter - but seems we are out of options here - that's kind of sad..

Thanks everyone, this question got out of hand here - but promise i will not ask more questions :)

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    $\begingroup$ You are heading outside the range of "conventional" engineering here. A pressure of 500,000 psi would permanently compress the material making solid block of steel (i.e. the casing for the pump, not the part you wanted to cut) So your first problem would be to find a suitable material to even start designing the pump (and don't propose "diamond" - the strength of diamond changes by a factor of 100 or more depending on the orientation, which is why "diamond cutting" for jewellery can be done using hand tools!) $\endgroup$
    – alephzero
    Commented Jul 15, 2017 at 0:30
  • $\begingroup$ Just to give you some intuition of what these high pressures mean, scuba diving air tanks are typically rated at about 3000 psi or a bit higher, so your target of 500,000 psi is 150 times higher than that. $\endgroup$
    – alephzero
    Commented Jul 15, 2017 at 0:35
  • $\begingroup$ hammelmann.de/en/produkte/hochdruckpumpen/uebersicht/… pumps capable of 3800 Bar, but what is the flow rate you need? Also do you have a 500kW supply? $\endgroup$
    – Solar Mike
    Commented Jul 15, 2017 at 8:11
  • $\begingroup$ @SolarMike but the OP wants 33,000 bar, not 3,800! $\endgroup$
    – alephzero
    Commented Jul 15, 2017 at 11:08
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    $\begingroup$ You missed the point - if you cut from the two sides then you will end up with a gap in the middle... I suggested " two jets half the length of the rock apart" so one starts at one end while the other starts in the middle... Shame that you did not provide real evidence of your process which would lessen the confusion. A further question is do you have a large enough power supply to create 33000 Bar as you want? $\endgroup$
    – Solar Mike
    Commented Jul 15, 2017 at 22:34

3 Answers 3

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I think the theoretical limit is based on materials, as alephzero said. You have to make it out of something, and the yield strength of the material will have to be greater than the internal pressure. There is a practical limit as well, because there has to be a margin of safety - at such high pressures the system would fail catastrophically if the pump or piping ruptured. If you use a factor of 3, which is fairly common, that means you need a material with a yield strength of 1,500,000 psi. Steels are typically something like 70,000 psi. Titanium might be 150,000 psi. I don't know where you go next, but that's what you'll need to look for.

When you say that cost and metal fatigue are secondary, keep in mind that even if the machine cuts metal 5 times faster than anything else when it's running, it really doesn't gain you anything if it's shut down for maintenance and replacement of major components for four days every week.

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  • $\begingroup$ your answer is much clearer - i only read it after i made that edit :).. My question may have changed a bit. Seems we can't get any better then the cutting speeds we already have? When you say steal has 70,000 psi aprox limit - what wall thickness you are referring for that pump? 1 cm - or 10 cm - Or you are referring to something else - the fact that even the piston leg will be crushed by this pressures ? Do you personally think we have a way to get this cutting 10x faster - or that is not even a thing to consider? Thank you. Sorry for my insistence - it's rely important :) $\endgroup$
    – AIon
    Commented Jul 15, 2017 at 14:33
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    $\begingroup$ Theoretical strength of materials is estimated as elastic modulus divided by 10. The material with highest elastic modulus is probably diamond (or graphene or nanotubes, but those have other manufacturing problems) at about 1220 GPa. Divide by ten, 120 GPa, gives 170 million psi. Granted, that's plenty, but theoretical strength far outstrips practical strength due to inherent flaws in brittle materials, and dislocation slip in metals. Nothing can be done about either with our present understanding! At best, reduce by a factor of several hundred for metals, or several thousand for brittle stuff $\endgroup$
    – do-the-thing-please
    Commented Jul 15, 2017 at 15:16
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    $\begingroup$ @AIon - Wall thickness doesn't matter if you try to contain a pressure that's greater than the yield strength. The material will permanently deform no matter how thick it is. I confess that I know nothing about abrasive cutting, but there are a lot of other issues too. For example, the nozzle will erode much faster at higher velocities. You'll nee an extremely hard material to resist the erosion. $\endgroup$
    – Mark
    Commented Jul 15, 2017 at 16:51
  • $\begingroup$ @Mark - i think i understand now what you mean. It's like i'm trying to contain a gas bubble in a soft mud. No matter how much mud i add around it - i can't contain it. That bubble will make it's way trough the mud until it finds the escape. maybe not the best example. But regarding that nozzle - will be industrial diamond - it's even harder that the naturally occurring one - because is 99.99% pure and has the right crystalline structure.. I found a company that produces this specially designed nozzles for water-jet cutting so that part is handled. They say it lasts 5 yeas - more then enough $\endgroup$
    – AIon
    Commented Jul 15, 2017 at 19:50
  • $\begingroup$ I stumbled across this question, your claim is discussed here engineering.stackexchange.com/questions/37024/… - maybe you want to join. $\endgroup$
    – mart
    Commented Aug 6, 2020 at 13:33
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Based on your last edit adding reasoning about the effect of diameter / flow rate etc, I would suggest you should seriously look at cutting with two nozzles at the same time - your analysis based on all the other answers / comments doesn't leave much else.

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  • $\begingroup$ thank you for help, yes that will work - somewhat - the thing is - i imagine this machine to be used for digging tunnels - a replacement for TBM's - so it's not a real water jet on a table - its much more complex, multiple jets, intersecting, controlled by an AI that will optimize their power and direction.. depending on the solid in front of it.. etc. Too complicated to explain here. Bottom line is - if we can cut faster - we can dig tunnels faster. So i just wanted to understand if we are at the maximum limits of this tech. And we are. It's so strange. I feel small, sad and humbled :( $\endgroup$
    – AIon
    Commented Jul 17, 2017 at 14:34
  • $\begingroup$ I will keep you in the loop once this 3d design is finished. There are tons of other problems with this idea. not sure if it actually makes sense - i will ask around once i have something concrete to show in terms of design. But know for sure now that we have a hard limit on speed that can't be overcome by just cranking up the power / build better pumps etc. We'll see. $\endgroup$
    – AIon
    Commented Jul 17, 2017 at 14:39
  • $\begingroup$ When you point a jet of water at the rock in the image - the water has somewhere to go, so if you are using it as a boring machine what happens with a blind hole? $\endgroup$
    – Solar Mike
    Commented Jul 17, 2017 at 14:39
  • $\begingroup$ there is no way around that - it slows down the cutting even more but is not stoping it. The trick is to point jets at an angle - because there will be multiple jets - one jet cuts the rock that is in front of another - so no one is pointing at 90 degrees. And this happens in 3d not in plane. This way the water will not push into itself. Again hard to explain without a 3d model. I did not thought about everything yet. But we'll see. $\endgroup$
    – AIon
    Commented Jul 17, 2017 at 14:55
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It is theoretically possible to drive a water jet to pressures of, say, 7,000,000 psi using explosives with a high detonation velocity, the shaped charge effect and a single use device. Higher pressures may well be possible with money, effort and optimization, for example swapping the RDX-based explosives in common shaped charges (detonation velocity around 8 km/s) with octanitrocubane (10 km/s).

Conventional shaped charges drive parts of the metal liners to velocities around 7-14 km/s. As the density of these liners (usually copper) is much higher than water, we may expect water's maximum possible explosive-driven velocity to be even higher. However there are other issues such as vaporisation of the water when a shockwave passes through it (reflecting off the free surface as a rarefaction wave), but you're still projecting "water" albeit in the vapor phase. For argument's sake let's start at several km/s. From there you can estimate the dynamic pressure by 0.5 x density x velocity^2.

At these pressures, struck materials behave like fluids and yield may be ignored as a good approximation. In fact - based on my experience simulating exploding and imploding systems driven by high explosives - you get good approximations to reality by treating the impact as fluid or particle-based. You won't need any sand in the water here and the cutting would be almost instantaneous :)

Yes, there are explosively-driven water jets out there, mostly for niche applications like disposal of IEDs by severing the detonation train. It was found that water jets, even those traveling at a few km/s, are not likely to initiate explosives compared to say metal jets traveling at the same velocities.

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