impact of sphere on water

[tbwttihs]

Does anyone know how I can calculate the impact force/energy of a sphere falling onto a fluid?

I know the geometry and mass of the ball, the height it has fallen (so can calculate a velocity at impact), and i know the properties of the fluid its being dropped onto.

the real life situation is a frac ball being dropped down drill pipe when the mud level in the drill pipe is about 150m below drill floor. I am trying to calculate, knowing the impact strength in ft-lb/in of the ball, whether this would be enough to fracture the ball.

 

[IRstuff]

Water has a density of 997 kg/m^3. Therefore, a volume of 97.7 cc of water must have mass of 97.4 gm. with a specific gravity of 3.4, its mass is therefore 0.33 kg.

TTFN

FAQ731-376

 

[handleman]

rb1957, what planet are you on?

One kgm weighs 1kgf here on earth where g=9.81. Sounds like you're on some planet with a gravitational constant 10 times that...

 

[zekeman]

rb1957,
You can't use the terminal drag force for the drag term since the velocity varies along the path; so you have to write a diff equation for that.
mvdv/dx=mg-kv^, e.g.
which is simple to solve.

 

[zekeman]

correction
The drag term is kv^2, not kv^

 

[prex]

As the free fall velocity of a human body (with legs and arms outstretched) is of the order of 50 m/s and the terminal velocity corresponding to the height of 150 m is about the same, I would say that the effect of the drag force by air is quite negligible here.
Now, craigp83, your problem is associated IMHO with the impact toughness of your metal filled phenolic plastic. If you can estimate that (or determine it by test) you would get an estimate of the energy necessary to break the ball, corresponding to the limit case of the mud behaving as a solid body.
If it was a steel ball with a typical toughness of 25 J on a 10x10 mm specimen, an energy of some 600 J would be required to break your ball into two halves, somewhat higher, but with the same order of magnitude, as the energy of the ball at impact.
So, if the toughness of the plastic is substantially lower than that of steel (as I expect, but have no data to offer), then you should expect a failure.


prex

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[jistre]

Here's my crazy suggestion.

You said that normally, the fluid level is at the drill floor, but due to additives to the mud (I'm assuming it made the mud denser, which weighed down the whole fluid column, pushing it down) when you guys dropped the plug in, it was 115m lower. If possible, couldn't you just bring the fluid level up higher so the ball doesn't fall as far before it hits the fluid? Seems to me that floating water on top of the mud should do the trick.

However, I'm not a petroleum engineer, so I don't know what doing that would mean to the mud or the hole.

 

[tbwttihs]

rb1957 - yes, you're right. for final clarification the ball has a mass of 0.3kg.

prex - yeah, i'd considered doing a drop test. I think we're sort of short on these things at the moment though so I'll wait until we get some spares in before I go breaking any more.

Jistre - yes, the idea is that the fluid should be at drill floor level and we will re-iterate this to the operator.

 

[rb1957]

ok, i made a mistake ... i agree the weight of 1kgm is 1kgf, so the mass is 0.3kg;

and yes, the way i accounted for drag was conservative.

how about instead of dropping the ball, could you lower it (attached to some string, or something) ?

 

[dvd]

Realistically it seems like the sphere is going to experience hits on the pipe joints that cause very high stress concentrations long before it hits the drilling mud. I don't imagine that the drill pipe is perfectly plumb so the sphere is going to bounce its way to the bottom.

 

[KENAT]

Why not experiment?

Do some controlled drops to validate calculations.

If nothing else drop it our of a top floor building into a bucket of water (or mud) and see if it survives.

To make sure it hits the water use a guideline (simplistically tape a bit of a drinking straw to each side of the sphere. Have 2 parrallel lines (fishing line or similar) from drop height down to the bucket.

Try and record velocity or related if you can.

KENAT, probably the least qualified checker you'll ever meet...

 

[FoMoCoMoFo]

your typical billiard ball is a 2-1/4" phenolic sphere, relatively inexpensive, durable and readily available but maybe not heavy enough (150-175 G's) certainly heavier than water but not sure about your mud. anyway I'm with dvd, sounds like its encountering shock more severe than simple 150m free fall into water