If I have a 9.964 gallon pressure vessel charged to 3514.7 psia, and I use it to fill an accumulator that is 1 gallon at 1214psia, what is the new pressure of the vessel?

I used, ((P1 X V1)-(P2 X V2))/V1

Is this an accurate formula? Also, how would I factor in temperature? Basically, I want to see what pressure/temperature there will be in the accumulator right after charging it, and then the next day as it equalizes to room temperature.

The Dalton's law of partial pressures) states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture, therefore
First partial pressure =(P1xV1)/(V1+V2)
Second partial pressure = (P2xV2)/(V1+V2)
the correct formula for the total pressure could be ((P1 x V1)+(P2 x V2))/(V1+V2)

Luciano

If I understand the question right - you want to know the final pressure in a nitrogen tank after charging an accumulator. You need to know the change in volume of the gas in the tank - how much you started minus how much you used.

Use Boyles law (P1*V1=P2*V2)to calculate volume of gas at STP, (standard temperature and pressure - I will assume pressures remain unchanged and can neglect it - standard pressure is 1 atm = 14.7 psia) calculate change in volume at STP - then recalculate pressure at the original volume.
Ok - first get the right units. Volume is in cubic feet and 1 gallon = .1336 cubic feet. Now we need the total volume of gas at STP. therefore v2 is the voulume of gas at atmosperic pressure that is in the 9.64 gallon container. Use Boyles law P1*V1=P2*V2 (3514.7*1.332)/14.7) and we get 318.47 cubic feet. Now - how much gas did we remove to charge bottle 2? We charged accumulator from 0 psia (You didn't specify initial pressure so I get to pick - although a starting pressure of 14.7 means a minimal difference here.) Again (.1336*14.7)/1214.7 = 11.05 cubic feet to charge accumulator #2. Now subtracct the gas used from the initial volume 318.47-11.05 = 307.42 cubic feet. Use Boyles law yet again to calculatye final pressure (307.42 * 14.7)/1.332 = 3392.7 psia.

The ending pressure in the 9.64 gallon bottle is 3392.7 psia or 3378 psig.

Is this charge and discharge fast enough to require accounting for temperature? pv = nrt, adiabatic process? the charging tank will be cooling and charged tank will be heating.

After the certain time has elapsed, then I agree the temperature correction drops out.
And in reality, the temperature effect will usually be ignored anyway. Just a theoretical point.

quote:

Originally posted by kevin j:
Is this charge and discharge fast enough to require accounting for temperature? pv = nrt, adiabatic process?

I don't treat charging accumulators as an adiabatic process. I do assume the pressure changes with a machine cycle are adiabatic.

quote:

the charging tank will be cooling and charged tank will be heating.

Yes, so it isn't adiabatic is it? However, do do not feel the accumulator temperature changes withing a cycle so that on can assume it is adiabatic or nearly so.

quote:

After the certain time has elapsed, then I agree the temperature correction drops out.
And in reality, the temperature effect will usually be ignored anyway. Just a theoretical point.

???? You don't think it makes a difference when you charge at 70 degrees and run at 120?
The air will heat up. In any case you should do the math once just to see how big a difference it makes when you ignore the difference between precharge temperature and running temperature.

I didn't check EdAllen's math but he is taking into account that the calculation must be in terms of absolute rather than gage pressure.
I like the simplicity of Luciano's explanation.
but it doesn't take into account temperature changes.

Josh, you use PV=nrT as Keven suggested. Where T must be expressed in Kelvin ( K ) or Rankine R.
Now for extra credit, how does one modify Luciano's equation to take into account the difference between the temperate at precharge and the temperature when running? Some algebra is required

One of the hydraulic power plants I worked with had a nitrogen precharge of 235 BAR at a temperature of 68 F. Pump compensators were set at 295 BAR. If the room ambient temp went above about 75 F, the resultant change in precharge would cause the "fully charged" nitrogen pressure to exceed the 295 BAR value, preventing the pumps from fully charging the piston accumulators.
By the way - Josh's question said nothing aboout operating parameters of either reservoir - I aassumed he was asking for steady state conditions.

quote:

Originally posted by EdAllen:
One of the hydraulic power plants I worked with had a nitrogen precharge of 235 BAR at a temperature of 68 F. Pump compensators were set at 295 BAR. If the room ambient temp went above about 75 F, the resultant change in precharge would cause the "fully charged" nitrogen pressure to exceed the 295 BAR value, preventing the pumps from fully charging the piston accumulators.

Josh, why don't you post this question at eng-tips.com or even plcs.net. I bet you will get the answer faster at plcs.net.

That is a good example of why one should at least consider the temperature changes.

quote:

By the way - Josh's question said nothing aboout operating parameters of either reservoir - I aassumed he was asking for steady state conditions.

I didn't assume that because he asked about how to compensate for temperature changes. One should be able to come up with a symbolic answer that is just an enhancement of the equation Luciano posted.

Bud, this isn't really a hydraulic question. This is the kind of question you get in a physics class.

Peter quipped:

quote:

Bud, this isn't really a hydraulic question. This is the kind of question you get in a physics class.

Probabbly would be a BIG part of a Fluid Power Engineer or Maintenance Persons TRAINING IF THERE WERE SUCH PEOPLE IN THE WORLD!!!!!!!!!!!!

I truly wish I would have taken a lot more formal TRAINING and also had paid more attention and had the opportunity to use what I did learn. I would'nt have so much trouble with formula that are much more complicated tha F=PA or GPM=GPI*IPM.

I could say I'm too old to learn, but the truth is I just don't have the desire.

I do have the free computer programs from Greer, Parker and Tobul to size Accumulator applications. All I have to do is plug in the numbers to get a part number of an Accumulator. I usually use at least two of them to double check the answer to make sure I didn't put a number in wrong.

So far the process has never failed to make the system perform as requested. I'm sure some were overkill but no one ever complained, except maybe a little bit about the price.

BUT, that is the way it is in a Field of Endeavor that has little FORMAL TRAINING and no one DESIGNATED AS ENGINEER OR MAINTENANCE PERSON.

Just put an ad in the paper and hire anyone who can spell Hydrolic, Hydroulic, Hydraulic and send them on their way. They will have to deal with only a minimum of persons who know more about Fluid Power than they do after they went through the company school for a couple of weeks and learned how to read the catalog. I trained several of these new sales persons myself after being in my territory for 3 years.

Oh Well Someday Maybe?????????????????????

I forgot 1/2 answer
To evaluate the temperature influence, the initial conditions determine the final results.
So I assume when you precharge bottles and accu are both to the same ambient temperature.
15 - 30 min after precharging the gas temperature equalize again and it is possible check the precharge pressure always at ambient temperature

to calculate the working precharge pressure when the gas temperature increase, I used the following formula:

Ap = Ambient precharge pressure (bar or psi)
Wp = Working precharge pressure (bar or psi)
AT = Ambient Temperature (°C)
WT = Working Temperature (°C)

Wp=Ap ((WT+273)/(AT+273)) (bar or psi)

I never seen on the drw which is the ambient temperature precharge pressure in order to obtain the correct working precharge pressure. So the math is left to the pipefitter, the result is random value of the precharge pressure
and when necessary subsequent correction.

Luciano

The temperature correction formula works and is the answer Josh's question about compensating for the difference between operating temperature and ambient temperature.

quote:

I never seen on the drw which is the ambient temperature precharge pressure in order to obtain the correct working precharge pressure.

What is drw? A graph?

quote:

So the math is left to the pipefitter, the result is random value of the precharge pressure
and when necessary subsequent correction.

Luciano

I don't understand what you mean by random?
You have provided all that is necessary as long as one waits for the temperatures to reach ambient.

BTW, for those of us using degrees F you need to change the 273 to 460.

I know, just buy a gauge!

The accumulators are for some sort of braking device for oil rigs; not too sure, I was just charging the accumulators for a work colleague.

Regardless, as I was charging them to 1200psig from a nitrogen tank with 3500 psig, I couldn't help but wonder what temperature the nitrogen was as it entered the accumulator, assuming it started at room temperature in the nitrogen tank. I also pondered what pressure the accumulators would be at the next day.

So specifically, my question is. Adiabatically speaking, what would the temperature of the nitrogen be instantly after charging the accumulator (to 1200 psi). Then - if it wasn't at room temperature at that point - what pressure will it be the next morning. I can figure out the second part if I know the temperature of the nitrogen after charging, I just can't wrap my head around what it will be.

I tried Dalton's Law as perscribed by Luciano, but my math didn't work out. Do I have to use cubic feet or can I use gallons?

My made up formula ((P1 X V1)-(P2 X V2))/V1
got me the same answer as Ed Allen's calculations. But that really still only gives me info for the storage tank. I'm more concerned with the temperature of the accumulator after charging now...

The process of charging the accumulator start at room temperature for both the bottle pack and accumulator.
At the very beginning the gas flow and expand at near adiabatic conditions from bottles to accumulator, the gas temperature lower but at different rates.

There is different temperature at the different points: inside the bottle pack, just after the reducing+needle valve, along the inteconnecting pipe and inside the accumulator, moreover the volume of gas originally contained into the accu, because is compressed, transforms some pressure energy into heat, also the external temperature can affect the process.
So there is no formula to calculate the instantaneous temperature and related pressure, the parameters are variable and the process ends just when the gas reach again the room temperature exactly like as when there is an isotermic transformation, it is a try and test process, require the necessary time to stabilize the internal temperature.

Bud explained how to test the precharge pressure without connecting to nitrogen side of the accumulator.
See the attached spreadsheet for numerical results

When I wrote:
"I never seen on the circuit diagrams (DRWG) which is the ambient temperature precharge pressure"

Was to prevent what happenet to EdAllen Who wrote:

"One of the hydraulic power plants I worked with had a nitrogen precharge of 235 BAR at a temperature of 68 F. Pump compensators were set at 295 BAR. If the room ambient temp went above about 75 F, the resultant change in precharge would cause the "fully charged" nitrogen pressure to exceed the 295 BAR value, preventing the pumps from fully charging the piston accumulators."

It is responsability of the project engineer set the correct precharge at ambient temperature and not live the pipefitter to guess the correct data.

Without correct information happen what described by EdAllen; on all drawings I saw was never indicated the precharge temperature togheter with the pressure.

Luciano

This message has been edited. Last edited by: Luciano,

Question_about_gas_laws__1.xls (40 Kb, 27 downloads) Excel

quote:

Without correct information happen what described by EdAllen; on all drawings I saw was never indicated the precharge temperature togheter with the pressure.

Luciano

Exactly.
On all schematics I include precharge pressure at 0 F, at 70F , and at 140F. For my world, those correspond to typical cold christmas break startup, average room temperature, and operating hot temp of the oil and tank.
k