Hydrostatic (distance of travel - molten metal in a tube out of a pressurized vessel)

CharlieNewman

Hello,
I'm a Process Engineer in an Aluminum Foundry and haven't been able to find the formula to solve the following problem and I'm hoping someone here can help. I've been digging through old text books, thinking this should be simple, but w/ no luck. - Thanks in advance.

I've got a vessel containing liquid Al (.085/in^3) that is pressurized w/ .1 psi of air (holds) and it forces the metal up a central tube to the atmosphere. What I'm trying to caclulate is the distance up the tube the metal travels above the original metal level. In our process, after each casting is poured (this is call a "Low Pressure Casting" process) the pressure in the vessel returns to a level slightly greater than the previous pressure (in this case .1 psi) based on the weight of the casting poured, to maintain the metal level the same distance up the tube.

I've tried to apply F= (A/a)*f and it is not caculating well.

If there is any more information I need to provide, please let me know.
Charlie

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Doc Al

I don't understand how a pressure of 0.1 psi can force the metal up the tube if the tube is open to the atmosphere (about 14.7 psi)?

CharlieNewman

It is a differential pressure, or an absolute of 14.8 psi. The pressure gauge reads like most commercial air pressure gauges. The actual pressure doesn't actually matter though, just the deviation from the surrounding atmosphere, because both the gauge and where the metal is going are under the same atmospheric pressure.

Doc Al

OK, the 0.1 psi was gauge pressure, not absolute. (That's what I suspected.) So the height of metal that such a pressure difference can support is given by P = ρgh, or h = P/ρg. (ρg = 0.085 lb/in^3; P = 0.1 lb/in^2) That comes out to about 1.2 in. (Is that anywhere close to what you observe?)

CharlieNewman

Absolutely! I've been wracking my brain for a day & 1/2. That was far too simple. So, the area of the metal/air contact area is negligible? How exactly does that work?

Thanks though; I'll plug that into my excel spread sheet. The PLC in this system calculates the desired "Pre-Pressure" (.1 psi at 95% full) based on the % of metal in the vessel, the casting weight, the capacity of the vessel, and the number of castings poured. This is done to keep the metal in the tube the same distance from the casting each cycle. I beleive at some point the vessel capacity value had been changed and I'm trying to correlate that w/ the way the casting is filled, based on the pressure curve used to fill the casting.

Thanks much,
Charlie