Calculate pressure after an orifice

[RasmusH]

Hi!

I have a system of piping going from a pressurized 80L cylinder with 300bar with a gas. In the system i have two orifices. First of I want to calculate the pressure and valocity of the gas after the first orifice, so I can calculate the flow of gas after the second orifice. I am not sure what equations i can use to find the pressure after the orifice.

Can anyone point me in the right direction, so i can dimention the needed sizes of my orifices?

Thanks!

 

[Latexman]

I will point you to two places. FAQs and Search. They are under the title of this thread, between Forum and Links.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

 

[LittleInch]

Do a search on restriction orifices here and globally. you need to use a gas flow rate to calculate pressure.

Remember mass flow rate will be the same through both.

Don't start with too many unknowns

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[davefitz]

Considering multiple sequential orifices, theoretical thermodynamic considerations indicate the choked flow location will be at the smallest sized orifice. The velocity will be mach 1 at that location and all other pressures can be calculated based on that pressure requirement. If you know the gas's molecular weight and temperature you can calculate its soundpseed and the choked mass flow ( kg/s/m2) vs P, and knowing the orifice minimum area determine the P at that orifice . The iterative correction that might be needed is to account for joule-kelvin cooling as the gas pressure drops.

"Nobody expects the Spanish Inquisition!"

 

[RasmusH]

thanks for the replys and sorry for the late answer.

I little clarification

@dave

Lets consider the first orifice. i have 300bar going in, I am assuming, that the flow will be choked giving me

P.crit=0.528*P.0 (for air)

Can i then say, that my pressure after the orifice will be:

0.528*300bar=158.4bar

In my optic the backpressure should depend on the size of the orifice.

I know that the velosity of the gas will be M=1, but i cant find a equation that calculate the backpressure from the velosity.

And can anyone confirm, that my flowrate will be the same through both orifices, which make sence to me?

Thanks a lot!

 

[eduvillela]

If both orifices are in series, then certainly the flow rate must be the same through both. Unless there's leakage..

 

[LittleInch]

I think you're looking for the wrong thing.

In a steady state run, the only thing you have as a constant is mass flow, not volumetric.

The pressure on one side of the first orifice is 300bar. The pressure on the far side of the second orifice is??? - you don't say.

The pressure in between the two orifices can be anything you choose. What it is will vary depending on the relative size of orifice,

As the pressure decreases, the density decreases and hence volume increases.

You just need to choose two orifice sizes and then keep adjusting the pressure until the mass flow rates get close.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[RasmusH]

Littleinch@

the upstream pressure to the first orifice is 300bar and the downstream of the second orifice is to atmosphere so 1 bar.

Can i assume, that the flow over both orifices will be choked?

and can you point me in the direction for the right equation for calculating the pressure between the two orifices? I have trouble calculating it for choked flow?

thanks a lot!

 

[LittleInch]

The second orifice is almost certainly choked flow if your DS pressure is 1bara.

however, as I said above, depending on the size of your first orifice it might be choked, it might not.

The aim for two orifice systems would normally be to try and split the pressure drop between the two to stop one being very small and one quite big.

Note that that is a large pressure drop and the erosion of a standard plate orifice will be significant.

Simply search for "restriction orifice" on this site or in google ( or your search engine of choice" and you will find many equations and on line calculators. There are two versions of the calcs, one for choked flow and one for not choked.

See this as a typical

http://www.engineeringtoolbox.com/flow-coefficients-d_277.html

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[RasmusH]

Thanks for your reply! but i cant seem to find a calculator, that calculates det downstream pressure. i can find the massflow. can you point me in the direction of an equation?

sorry for all the questions!

 

[3DDave]

In choke flow the downstream pressure is the downstream pressure. Choked flow through an ideal orifice doesn't/can't affect downstream pressure.

"Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed."

https://en.wikipedia.org/wiki/Choked_flow

This might also help:

https://en.wikipedia.org/wiki/Orifice_plate

Orifices aren't an analog to electrical resistors. They don't just add together.

You'll have to work backwards and look at mass flow rate, knowing that the same mass is flowing though both orifices and then determine whether the pressure difference at each orifice is sufficient to produce choked flow. It's non-linear so there isn't a simple equation to solve for the conditions. Were it up to me I'd put the equations into a spreadsheet and make a plot of the mass flow rate vs pressure drops until it met the other conditions.

 

[RasmusH]

@3d dave

"In choke flow the downstream pressure is the downstream pressure. Choked flow through an ideal orifice doesn't/can't affect downstream pressure."

Do you mean, that when the pressure is choked, the downstream pressure will be a constant not dependant on the upstream pressure as long as there is choked conditions?

I have read those wiki pages. my problem is, that i dont know which equation i need to calculate the pressure drop?

Thanks !