jet of fluid from punctured tank 1

[alpipe]

Having been challenged by the client regarding tank spacing in bunded areas it would be useful for me to be able to calculate the maximum distance a jet of fluid could move horizontally from a punctured tank before hitting the ground. I am trying to keep this simple and generic, but lets assume a 50mm dia hole located where ever this dist would have the greatest effect, and the media is water, atmospheric tank.
Cheers

 

[sailoday28]

With little resistance from the surrounding medium (air), how far could you throw a projectile if you have the angle of depression/elevation and initial velocity of the object?

 

[BigInch]

Take the head above the hole and subtract the outlet coefficient head loss. Calculate the time it takes for the fluid to hit the ground from the height of the hole. Convert the remaining head above to velocity (Bernoulli equation) and multiply the velocity by the calculated time to find the horizontal distance traveled.

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[dickon17]

BigInch has it exactly right. If you need help with Bernoulli and you can live with a close approximation, use the following simple equation to calculate velocity.

Velocity = 8.0 X square root head of water.

For a tank with 100 feet of water above your 2 inch hole, velocity would be about 80 feet per second. If you noticed, the size of the hole does not affect the velocity (only the volume).

 

[chemroopa]

USe Bernouli's equation with ruptured point as your datum and liquid surface as the other point where velocity is zero. you know head and the pressure acting on the surface. I guess it would be a closed tank with N2 blanketing . At datum, given pipe size, find the velocity and find the time to hit ground at trajectory path. Velocity over time will give you the distance you want to know.

 

[kenvlach]

If Nuclear Enginers find intro. fluid dynamics challenging, perhaps we should fear a Big Bang?

 

[BigInch]

Then let's hope the tank engineer gets it right and there is no leak.

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[athomas236]

You could try this link

http://www.lmnoeng.com/TankDischarge.htm

athomas236

 

[BigInch]

nice ref. everything, one page.

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[25362]

Somehow, it resembles prostatitis.

 

[Cockroach]

If the hole is small and on the side of the tank, use v=Cv sqrt(2gH) for H=height of fluid ABOVE the hole, Cv=velocity coefficent (=0.97 for water) and v=fluid jet velocity.

Large punctures v=0.667 Cd b sqrt(2g(H^3/2 - h^3/2)] for b=width of puncture, H=fluid height above bottom of hole, h=fluid height above top of hole and Cd=discharge coefficent (=Cc Cv, Cc=0.62 sharp, 0.97 rounded edge hole)

Given the velocity of the stream, a particle of fluid can be treated like a solid body moving through a uniform gravitational field. In the case of a small aperature, the maximum horizontal displacement is s=2 sqrt(H h) for H=fluid height above hole, h=fluid depth below hole. In the literature this computation is called "Ohne Jegliche Reibwerte", for your cultural entertainment.

Good luck with it. Very nice problem.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[hydtools]

I happened to be going through an old text book that addressed this condition. An atmospheric tank containing water. The distance the water went is called range. The single equation solving for range is R= square root of (4*h*y). h is height of water above the hole. y is height of hole above the elevation where the water hits the ground. Units are in feet.

Most interesting is the conclusion that the greatest range is when h=y. That is the hole is midway between the free water surface and the ground. This is really the worst case for the question of how far the stream will reach. All other cases result in the stream hitting closer to the tank.

The book is an 1897 edition of The Elements of Mechanical Engineering.

Ted

 

[athomas236]

hydtools,

1897, gosh those old guys knew nothing and not a sreadsheet in sight.

just joking

athomas236

 

[rcooper]

Couldn't you get a different (possibly worse) condition if the hole is not horizontal, but deflects the jet of water slightly upwards? If the hole was at ground level, then the worst case deflection would be 45 degrees, giving the furthest travel, but I would have throught this would vary with different positions in the tank wall. Time for partial differential equations to find the worst case.

 

[hydtools]

rcooper, I think you are expanding the original problem. A simple puncture 50mm hole somewhere on the side of the tank. What would be the farthest horizontal distance the jet of water would go.

I agree that a jet exiting from the bottom at a 45 degree upward angle would go the farthest horizontal distance. That is consistant with what we learned about simple projectile trajectory analysis.

Ted

 

[BigInch]

Considering that most tanks in bunded spaces don't make holes shooting from 45º to the horizontal, I think 0º has the greatest reasonable probability. Also rather obvious that a hole in the tank roof is just going to make rain, if there is any liquid that high up there to begin with. Horizontal bullets, I would think probably blow on the bottom half somewhere and the top half is more likely to contain vapor anyway... or will pretty quickly.

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[rcooper]

BigInch,

0 degrees has the greatest probability as you state, but as the hole gets smaller I believe the distribution of the discharge angle will increase due to surface tension effects and the shape of the hole. I can't prove this, but from my observation of leaks I would be surprised if we can state that 0 degree discharge from the tank is the only angle of discharge.

Therefore to answer the original poster's question to give a worst case area for the bund, the varying degrees of discharge should be considered, and only discounted if proved insignificant.

 

[BigInch]

You might have a point about the surface tension and all, but I think only if there is very little pressure behind it where the surface tension (or whatever) might control. Actually I think its the liquid level static pressure distribution above and below the hole that might affect the location of the vena contracta. Wouldn't a lesser velocity towards the top of the hole and a higher velocity towards the bottom of the hole tend to curve the jet upwards?

In any case, I agree 0º does not yield the most conservative result.

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