Time taken by gas to fill empty vessel

In summary, to calculate the time required to fill an empty vessel connected to a pipeline with gas at pressure P, you will need to know the cross sectional area of the pipe, volume of the vessel, atomic mass of the gas, and final temperature. Using the ideal gas law, you can estimate the time it will take for the vessel to fill up, but the actual time may vary due to factors such as particle flux and mixing.
  • #1
ank160
21
0
Suppoese there is a empty vessel connected to a pipeline having a continuous supply of gas at pressure P. Gas will continue to move in vessel till pressure in it become P. How to calculate time required to fill the vessel completely.

Plz help.
 
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  • #2
hi ank160! :wink:

show us what you've tried, and where you're stuck, and then we'll know to help! :smile:
 
  • #3
You've not given enough parameters to perform the calculation.
 
  • #4
This question can only be answered very approximately. You need the cross sectional area of the pipe (A), the volume of the vessel (V), the atomic mass of the gas (M), and the final temperature (T)

The momentum flux of the gas at the outlet of the pipe is P*A. If you divide out the atomic mass, you can get the particle flux.
So, calculate how many particles are in the vessel at temperature T, pressure P using the ideal gas law, and then you know how long it will take (roughly).

In reality, the particle flux will slow down as the vessel fills up, and the vessel won't necessarily mix fast enough to have a well defined pressure or temperature for a bit. I would multiply the result by a factor of e just for the hell of it.
 
  • #5


The time required to fill the vessel completely will depend on several factors such as the volume of the vessel, the flow rate of the gas from the pipeline, and the pressure inside the vessel. To calculate the time, we can use the ideal gas law which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Assuming that the temperature remains constant and the vessel is initially at atmospheric pressure, we can rearrange the ideal gas law to solve for the time (t) as t = V * (P/Pipeline pressure) * (RT/Pipeline flow rate). This equation takes into account the volume of the vessel, the pressure inside the vessel, and the flow rate of the gas from the pipeline. However, it is important to note that this is an ideal calculation and may not take into account factors such as turbulence or leaks in the vessel that could affect the filling time.

In order to get a more accurate calculation, we can use experimental data to determine the actual flow rate of the gas from the pipeline and the actual pressure inside the vessel as it fills up. This data can then be used to calculate the time required to fill the vessel completely. Additionally, we can also use computer simulations to model the filling process and get a more precise estimate of the time required.

I hope this helps. Please let me know if you have any further questions.
 

1. How does the temperature of the gas affect the time it takes to fill an empty vessel?

The temperature of the gas has a direct impact on the time it takes to fill an empty vessel. As the temperature increases, the molecules of the gas gain more kinetic energy and move faster, resulting in a faster filling time. Conversely, as the temperature decreases, the molecules slow down and the filling time increases.

2. Does the type of gas used affect the filling time?

Yes, the type of gas used can greatly affect the filling time. Different gases have different molecular weights and properties that can impact how quickly they fill a vessel. For example, helium, which has a lower molecular weight, will fill a vessel faster than a heavier gas like carbon dioxide.

3. What role does pressure play in the time it takes for a gas to fill a vessel?

Pressure also plays a significant role in the filling time of a gas. As the pressure increases, the gas molecules are pushed closer together, resulting in a greater number of collisions and a faster filling time. Similarly, a decrease in pressure will result in a slower filling time.

4. How does the volume of the vessel impact the filling time of a gas?

The volume of the vessel is directly proportional to the filling time of a gas. This means that as the volume of the vessel increases, the filling time will also increase. This is because a larger volume requires more gas molecules to fill it compared to a smaller volume, resulting in a longer filling time.

5. What other factors can affect the time it takes for a gas to fill an empty vessel?

Other factors that can affect the filling time of a gas include the size and shape of the vessel, the initial pressure of the gas, and any obstructions or obstacles in the vessel. The gas flow rate and the efficiency of the filling equipment can also play a role in the filling time.

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