How to Calculate Nitrogen Purge Velocity in Fixed Volume Tanks?

[bluesman4509]

This is not homework, but a problem from work.

If 4 tanks with fixed 90m^3 volume contained Nitrogen gas at 701.3 kPag were purged to 131.3 kPag through a 100mm pipe how would I work out the velocity/volumetric flow rate of the output?

Thanks

 

[Mech_Engineer]

As in similar threads, this problem is more difficult to solve than you might first think...

Here's a discussion on the subject of a pressure vessel depressurizing through an orifice:
https://www.physicsforums.com/showthread.php?t=363205

 

[mugaliens]

The velocity isn't dependant only upon the fluid (pressure, viscosity, density), and not just on the diameter of the 100mm pipe, either, but also the length of the tube, it's roughness, and the entry geometry (exit, not so much provided its flush or free air). Is the tube's entrance flush with the interior of the tank, or in free air?

 

[bluesman4509]

Thanks all for the pointers,

mugsliens I've completed a subject in fluid mechanics that only looked at incompressible fluids so would I be correct in saying that major (friction) and minor (inlet/outlet exspansions) head losses relate smilarly in compressible fluids?

I will receive data from some flow meters soon, since I read in another post that I would need to consider the change in temp. through the pipe I guess introducing measured data would make the theoretical calc useless anyways.

 

[alphy]

for reaching out regarding this problem from work. I would approach this problem by first understanding the concept of nitrogen purge velocity. Nitrogen purge velocity is the speed at which nitrogen gas is moving through a system during a purging process.

To calculate the velocity or volumetric flow rate of the output in this scenario, we would need to use the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT. In this equation, P represents pressure, V represents volume, n represents the number of moles of gas, R is the gas constant, and T is the temperature.

In this problem, we know the initial pressure (701.3 kPag) and volume (90m^3) of the nitrogen gas in each tank. We also know the final pressure (131.3 kPag) and that the gas is being purged through a 100mm pipe. To calculate the velocity or volumetric flow rate, we would first need to determine the number of moles of nitrogen gas present in each tank using the ideal gas law. We can then use this information to calculate the volumetric flow rate using the equation Q = n/t, where Q is the volumetric flow rate, n is the number of moles of gas, and t is the time it takes to purge the gas.

We can also use the ideal gas law to calculate the velocity of the gas as it exits the 100mm pipe. This can be done using the Bernoulli's equation, which states that the total energy of a fluid is constant. In this case, we can equate the initial and final energy of the nitrogen gas to calculate the velocity.

In summary, to calculate the velocity or volumetric flow rate of the output in this scenario, we would need to use the ideal gas law and Bernoulli's equation. It would also be helpful to know the temperature of the gas and the time it takes to purge the gas. I hope this helps in solving the problem at hand. Best of luck!