Calculating possible vacuum pressure

If the headspace is sealed then the pressure or vacumme in the headspace will be equal to minus the static pressure.

Mark Hutton

HEC,

When you say "minus the static pressure" are you referring to the surrounding static pressure? i.e. -14.7 psia if I am at atmosphere? Or static pressure in the vessel from liquid head?

When you drain the liquid out with no vent the pressure in the tank will sink to the vapor pressure of the liquid at the operating temperature. Realize that the temperature of the liquid will drop from the initial temperature as liquid vaporizes to fill the space. So to get the exact pressure you will have to to an energy balance.

Regards
StoneCold

StoneCold,

I apoligize for my ignorance. What exactly would this energy balance look like? Since I am draining, it seems that my mass will go to zero, and I will not be able to close the enthalpy balance on water.

Any help is appreciated.

Static pressure from the liquid, or atmospheric whichever is the lessor i.e. you cannot go less than 0kPa(abs). I agree with StoneCold, the head space pressure will be determined by the vapour pressure of the fluid. The head of fluid would be a starting point for the expected pressure. from there an iterative process may be required.

Mark Hutton

Ok
Start like this. What is the fluid? What is the operating temperature? Based on that you can find the vapor pressure.
Assuming the liquid volume is fairly large the flashing vapor will have little effect on the bulk temperature so for this first calculation we will ignore that problem. So the pressure in the tank will fall to the vapor pressure of the liquid as the liquid is pumped out of the bottom.

If the liquid drains out in 5 minutes or 5 days, if there is no leaks the answer is very close to the same pressure.

If it drained out instantaneously that would be a non equilibrium problem that would be more difficult to solve but the answer would be between the vapor pressure of the liquid and 0 psia.

Hope this answers your question.

Regards
StoneCold

david6425
Perhaps I can offer a few comments on your question and the responses you have received. Consider a vessel:
Tank volume= x cuft; 90% full (outage = 10% filled with air)
Ambient conditions: P = 14.7 psia; T = 530 R.
Tank drained (gravity or pump); no air ingress
From the gas law: P(2) = P(1)*V(1)/V(2). (volume is headspace)
From volume x: V(1) = 0.1x ; V(2) = x (empty)
Temperature at empty same as initial temperature.

P(2) = 14.7 * 0.1x/x = 14.7 * 0.1 = 1.47 psia
Depending on tank temperature and liquid stored there may be some amount of flashing which will make the final pressure higher than the 1.47 psia.

Tank pressure drops as headspace increases (level drops). Rate of drain only affects the rate at which the pressure drops. If drain is by gravity, then drain rate is given by the efflux equation. Drain rate by gravity is a function of the head of liquid in the tank. If the tank is an atmospheric tank, its mechanical integrity will be affected by the external pressure as the tank drains. Such a tank will buckle, collapse, and perhaps rupture if it is not rated for external pressure.

david6425
Perhaps I can offer a few comments on your question and the responses you have received. Consider a vessel:
Tank volume= x cuft; 90% full (outage = 10% filled with air) Ambient conditions: P = 14.7 psia; T = 530 R.
Tank drained (gravity or pump); no air ingress From the gas law: P(2) = P(1)*V(1)/V(2). (volume is headspace)
From volume x: V(1) = 0.1x ; V(2) = x (empty) Temperature at empty same as initial temperature.

P(2) = 14.7 * 0.1x/x = 14.7 * 0.1 = 1.47 psia
Depending on tank temperature and liquid stored there may be some amount of flashing which will make the final pressure higher than the 1.47 psia.

Tank pressure drops as headspace increases (level drops). Rate of drain only affects the rate at which the pressure drops. If drain is by gravity, then drain rate is given by the efflux equation. Drain rate by gravity is a function of the head of liquid in the tank. If the tank is an atmospheric tank, its mechanical integrity will be affected by the external pressure as the tank drains. Such a tank may buckle, collapse, and perhaps rupture if it is not constructed for some external pressure (vacuum).

you have water filled up to the tank at 90% where the 10% air space is atmospheric air. the level starts to drop. as soon as the bottom of your tank sees about 34' (14.7 psi converted to head) of head, you'll start getting air bubbles sucked into the tank outlet to equalize pressure. similar to if you ever bought one of those 2 gallon water jugs and tried to fill a glass without punching out the vent port

like the above posts say, what is left is the vapor pressure inside the vessel and the pressure of the air at the new expanded volume (assuming you don't consider the air coming into the outlet). At a max with water at 20 deg C youll see about 20 mmHg from the vapor pressure + the final pressure of the 10% air if you have a check valve at the tank outlet.


if this is a tank, id expect this to have PVSV on the top to make sure you didnt pull too much vacuum on the vessel, but assumptions above, you can pull pretty close to complete vacuum.


-Mike