Ronco Salami Slicer?

October 17, 2007 6:13 AM

Physics: Suppose I have a 10million gallon tank of H2O and I drill a 0.5mm hole near the bottom...

Will the resulting stream issuing from the hole have enough force that I could wave a salami in front of it and slice it?

- If not....how big of a tank of water would I need in order to slice salami? Or, how small of a hole? Or is there some limiting factor that would make slicing a salami in such a setup impossible?

posted by ian1977 to science & nature (43 comments total)

What kind of salami?
posted by chillmost at 6:19 AM on October 17, 2007 [4 favorites]

Also, are we presuming you're at sea level and that the tank allows air to flow freely in the space once occupied by water?
posted by beaucoupkevin at 6:24 AM on October 17, 2007

A Platonic ideal of salami.
posted by ian1977 at 6:25 AM on October 17, 2007 [9 favorites]

Is the tank 1 mile wide and a 1/2 inch deep or 1 mile tall and 1/2 inch wide?
posted by Slenny at 6:25 AM on October 17, 2007

Yes. Sea level. And the top of the tank is open to atmosphere.
posted by ian1977 at 6:25 AM on October 17, 2007

It's not the volume of your tank that will determine the outflow velocity, but the height. If you ignore any losses (which is doubtful with such a small hole!), a first estimate is given using Bernoulli:

v = sqrt (2gh)

The momentum contained in the flow would be the density times the velocity squared times the cross-section of the jet. I haven't got a clue about the material properties of salami (yield stress?); I now have a nice idea for a student project, however!
posted by swordfishtrombones at 6:29 AM on October 17, 2007

Slenny....good question....

The tank is 10x4 feet wide and .....according to my very crude calculations....400,000 feet tall. (assume atmosphere pressure maintains even at this altitude)


gallons/0.625=Cubic Feet

10,000,000/.625=16,000,000 Cubic ft.
posted by ian1977 at 6:29 AM on October 17, 2007

Okay....lets turn the tank into a dam instead.
posted by ian1977 at 6:30 AM on October 17, 2007

You need to think about the shape of the tank, as far as I can work it out. The two factors that will turn your hole into a waterjet cutter are it's size and the pressure acting on the water behind it.

You've already got a small hole, so you need to maximise your pressure. You need to do this by maximising the 'head' of water above the hole, so your tank needs to have a small base area, and be very, very tall.

You could, for example, hold all the water in a flat tank that's extremely wide and deep, but only a few inches tall. In that case your jet will just splash off the salami and get you wet.

So go for a tank that's cylindrical, with a small cross-section, but is extremely tall. In fact, a very long pipe. The limiting factor will be how you support your wildly non-sensible tank. And remember, a softer salami could save you a few stories' height of water in order to get the job done, so go to a good deli and try a few before you buy.

I think you need to go and borrow some piping from the nearest oil rig. You could lean it agains the Empire State Building for support. That might do the trick.

But do it, and do a FPP in the blue all about the resulting video you post on Youtube!
posted by dowcrag at 6:31 AM on October 17, 2007 [1 favorite]

swordfish....so a 1inch wide by 1 mile high tank will exert the same force as a 10foot wide by 1 mile high tank?
posted by ian1977 at 6:32 AM on October 17, 2007

I now have a nice idea for a student project, however!

I think another professor may have already beaten you to it.
posted by dead_ at 6:32 AM on October 17, 2007 [1 favorite]

By the way, have a look at this page about Torricelli's equation.
posted by swordfishtrombones at 6:32 AM on October 17, 2007

@dead_ - a professor went about finding the material properties of salami???
posted by ian1977 at 6:34 AM on October 17, 2007

From This page:

Water only cutting is by a high velocity fluid jet. Operating pressures are up to 3200 Bar generated by an intensifier pump giving a velocity at the work piece greater than twice the speed of sound.

[...]

Typical jet sizes range from 0.1mm to 0.25mm diameter. Single head and multi-head machines are available to cut prototypes or volume production.

posted by Jakob at 6:35 AM on October 17, 2007

swordfish....so a 1inch wide by 1 mile high tank will exert the same force as a 10foot wide by 1 mile high tank?

Yes, that's the hydrostatic equilibrium principle.
posted by swordfishtrombones at 6:35 AM on October 17, 2007

@Jakob - so gravity and air pressure would never be able to produce the pressures needed to cut a salami?
posted by ian1977 at 6:36 AM on October 17, 2007

Some discussion of this problem here is: Torricelli's Law. There's a better derivation here.

I don't know how much pressure you would need to cut salami, but apparently a high pressure water cutter is 30,000-60,000 psi.
posted by Comrade_robot at 6:36 AM on October 17, 2007

@swordfish Would it make a different if the tank were cone shaped? (with the nose pointing down)
posted by ian1977 at 6:37 AM on October 17, 2007

as slenny pointed out, what matters is how much water, in linear measurments, is above the hole, as this will provide the water pressure.
Goolge tells me 10 million gallons is 37 854.118 cubic meters, so we can begin with that number.
This question is also difficult because the general equation yields for a difference in pressure between the top and bottom of the column of fluid. Usually, that is enough of an approximationm, but here, you would have to know the pressure 37 854 meters up. You'd also have to account for the change in the density of water at different tempereatures (wiki). And you might have to consider the weakening of gravity when you get that high up. Complicated.

I dont know how to figure out how much force salami needs to be cut, on average.
posted by milestogo at 6:38 AM on October 17, 2007

@swordfish Would it make a different if the tank were cone shaped? (with the nose pointing down)

No, why would it? Google 'hydrostatic paradox' for some more explanation.
posted by swordfishtrombones at 6:40 AM on October 17, 2007

Would it make a different if the tank were cone shaped?

No. Here's one way to look at it: in a cone-shaped tank, not all the water will be resting on the nozzle/base of the tank; some of the weight of the water will be supported by the sides of the cone.
posted by DevilsAdvocate at 6:43 AM on October 17, 2007

Alright....looks like another get rich quick scheme foiled by science.

Oh well. Back to the drawing board. Thanks for dashing my hopes! :-P
posted by ian1977 at 6:47 AM on October 17, 2007

@Jakob - so gravity and air pressure would never be able to produce the pressures needed to cut a salami?

Alas, it looks like you couldn't in any practical sense. Omitting changes in air pressure and gravity with height the pressure at the bottom of a column is ?gh where ?= 1000 kg/m^3, g = 9.81 and h is the height of the column. 3200 bar is 32x10E6 Pa. Using this relation I get a column height of 3,262m. Which is a little tall for a practical tank.
posted by Jakob at 6:57 AM on October 17, 2007

Well, if you're looking to cut salami with water I think a pressurised tank would be more feasible than an open-air one... hand-operated pump, if electricity usage is an issue.

Is anyone going to test it out? The open tank should be substitutable for a water pump system, and with the appropriate measurements of pressure or exit velocity I think the results can be easily extrapolated for an open-air tank. Sounds interesting nevertheless... I think the choice of material for such a small nozzle would be a more provoking question though.
posted by kureshii at 6:57 AM on October 17, 2007

I know in automated food production they use water jets to cut all sorts of stuff, but I assume those are pressurized water jets.
posted by ian1977 at 7:00 AM on October 17, 2007

3200 bar is 32x10E6 Pa

I think you are missing a zero somewhere...

*goes back to grading homework*
posted by swordfishtrombones at 7:14 AM on October 17, 2007

I think you are missing a zero somewhere...

I knew I should have double-checked... absolutely right. In which case the water column is 36km high, and the water would be boiling off at the top.
posted by Jakob at 7:18 AM on October 17, 2007

What would be practical is to say, suppose you go down in a submarine that's kept at 1atm inside. And then at some very great depth, you open a tiny little valve leading to the outside -- how deep would you have to be, to cut (wood, metal, salmi, whatever) with it?

A good first-order approximation is that 10m in depth gives you about 15psi in pressure increase; therefore, 30000psi would be about 20000m down.

That's about twice as deep as the Marianas Trench (11km).

However, I suspect that you'd be able to slice a salami with a lot less than 30000psi, but you'd need to do some experiments to find out.

I think that you'd find that the actual salami-cutting depth was within the range of deep-diving submersibles (not that you'd really want to open a seacock in real life, of course).
posted by Kadin2048 at 7:52 AM on October 17, 2007

@Kadin - Perfect! An underwater salami cutting station.
posted by ian1977 at 8:21 AM on October 17, 2007 [1 favorite]

With 60,000 psi you can cut stainless steel with a water jet. Sometimes abrasives are mixed with the water. More..
posted by weapons-grade pandemonium at 9:22 AM on October 17, 2007

ian1977 we don't use the @username convention here. Just the username is sufficient.
posted by Mitheral at 10:47 AM on October 17, 2007

Mitheral - yikes! Sorry, thanks for the heads up.
posted by ian1977 at 11:38 AM on October 17, 2007

Sounds like a comment should be made for Mythbusters to do some research.

Just a thought!
posted by bach at 11:56 AM on October 17, 2007

Ian... what was this for? Was there a bet on this?
posted by JakeLL at 12:41 PM on October 17, 2007

I have some video somewhere of an ROV descending with some ping pong balls and Styrofoam cups . The ping pong balls didn't make it to 100m iir, and as any good subsea surveyor knows, the cups were little styrofoam shot glasses when we returned to the surface. Cute!

Interestingly, bathtub playthings made out of sponges are unaffected by the descent.
posted by MotorNeuron at 12:59 PM on October 17, 2007

Note that building a really tall tower in which to store water is in no way "free" in terms of energy. You spend exactly as much energy driving the pump that fills it with water from ground level as you get out of the stream that does the cutting. So this would be in no way free energy. If you were thinking of letting it naturally fill with rainwater, I think you will find that all kinds of nasty stuff would grow in there which would totally clog up whatever jet you used.
posted by Rhomboid at 2:13 PM on October 17, 2007

Jakell - I was reading a novel and the author used as a metaphor a pinhole leak on a dam having a tiny water jet that shot hundreds of feet into the air and I wondered if it such a jet could cut through salami.
posted by ian1977 at 2:15 PM on October 17, 2007

Note that said water jet would, in reality, shoot no higher than the top of the water behind the dam - you could conceivably get a jet hundreds of feet tall only if the dam were also hundreds of feet (or more) tall.
posted by DevilsAdvocate at 2:34 PM on October 17, 2007

DevilsAdvocate - By into the air I meant forward.
posted by ian1977 at 2:39 PM on October 17, 2007

The maximum horizontal distance is twice the height of the water behind the dam, assuming the ground/river/whatever the water's landing on is even with the bottom of the dam. (If it's below the base of the dam, the maximum horizontal distance is less than twice the difference in height between the top of the water behind the dam and the surface it's landing on.) If you want the water to shoot 300 feet forward, you need a 150-foot tell dam, or else a valley whose floor is more than 150 feet below the top of the dam.
posted by DevilsAdvocate at 9:12 PM on October 17, 2007

There is a Japanese program called "Trivia Stream" (Toribia no Izumi) or something akin to that - they had a segment where they wanted to know how much water pressure it would take to breach a porcelain urinal (I'm guessing much more difficult than slicing salami). They went off to some lab, and installed one of those "little pissing boy" statues onto a high power water jet. Then they ramped up the water pressure until it broke through the urinal. I can't recall what PSI it was, but you may be able to find the clip on YouTube or somesuch.
posted by birdsquared at 10:04 PM on October 17, 2007

Of course, the real question is whether cutting a tiny hole in a tank that side would cause the bottom to crack and shatter, creating a problem much more sizable than unsliced salami.
posted by softlord at 12:50 AM on October 19, 2007

I just spent a very long time trying to find salami statistics, failing, and then doing some math to try and figure out the pressure under a knife blade when you cut salami, and then figuring out from there what sort of water you'd need to do the same.

Then I realized that my initial assumption about the knife blade was wrong.

So I decided to have some ham instead.
posted by blacklite at 1:31 AM on February 5, 2008