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Jeirn
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Do you know where I can find a formula to calculate how long it would take to drain a cylinder under pressure to atmospheric pressure? if I know the volume of the cylinder and the size of the opening.
Are you to assume that the cylinder is insulated? Kept at constant temperature?Jeirn said:Do you know where I can find a formula to calculate how long it would take to drain a cylinder under pressure to atmospheric pressure? if I know the volume of the cylinder and the size of the opening.
If we assume constant temperature, PV=nRT, with V, R and T constant. The rate of escape will be proportional to the pressure difference, P-Patm.Jeirn said:Its a cylinder of natural gas...can you assume values and give an example of how to find time it takes for gas to fully escape through a hole in the cylinder. I know it's some kind of differential equation.
berkeman said:This doesn't look like homework.
haruspex said:If we assume constant temperature, PV=nRT, with V, R and T constant. The rate of escape will be proportional to the pressure difference, P-Patm.
##\frac{dP}{dt}=-k(P-P_{atm})##, for some constant k (which will depend on the nozzle).
All you are saying there is that initially the atmospheric pressure is so low compared to the pressure in the bottle that it can be ignored. So at that stage the equation I wrote is more accurate than what you propose.boneh3ad said:Actually, this is inaccurate. For a high-pressure cylinder such as a gas bottle, the pressure ratio is such that the flow would be choked and the atmospheric pressure is irrelevant. The rate of mass leaving such a bottle will depend only on the current pressure inside the bottle, the temperature inside the bottle, and the size of the opening. The ambient pressure only becomes relevant once the pressure drops to a low enough value that the flow is no longer choked.
haruspex said:All you are saying there is that initially the atmospheric pressure is so low compared to the pressure in the bottle that it can be ignored. So at that stage the equation I wrote is more accurate than what you propose.
At first, the additional accuracy is unnecessary, but since the question asks for the time to become effectively equalised, the more accurate form is required later. And since the one equation handles the whole domain, there is no benefit in handling the initial stage separately.
The timing for replacing an empty gas cylinder depends on the specific gas being used and the rate at which it is consumed. It is important to monitor the gas pressure gauge and replace the cylinder when the pressure drops below the recommended level.
The empty timing for a gas cylinder can be determined by calculating the consumption rate of the gas and comparing it to the amount of gas remaining in the cylinder. This can be done by dividing the total volume of the gas in the cylinder by the flow rate of the gas.
The empty timing of a gas cylinder can be affected by various factors such as the type of gas, the flow rate, the temperature and pressure of the gas, and any leaks or malfunctions in the equipment being used.
It is recommended to check the gas cylinder for empty timing regularly, especially before starting a new experiment or project. This will ensure that there is enough gas to complete the task and avoid any interruptions or delays.
Empty gas cylinders should be properly labeled and returned to the supplier for refill or disposal. It is important to follow proper safety protocols when handling empty gas cylinders to avoid any accidents or hazards.