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Mass flowrate and pressure at subsonic and supersonic speeds
- Thread starter JammyHam
- Start date
LittleInch
Petroleum
Need more details, but sounds like choked flow to me.
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
My motto: Learn something new every day
Also: There's usually a good reason why everyone does it that way
In choked flow and in supersonic flow the standing shock wave prevents downstream equipment from communicating back to the source (e.g., friction in downstream pipe is not a factor in the mass flow rate). In subsonic flow, the downstream effects are able to communicate back to the source and downstream effects do change mass flow rate.
This effect is vividly evident in a diverging nozzle:
[ul]
[li]For incompressible flow (i.e., velocity below about 0.6 M), an increase in cross sectional area causes a decrease in velocity at an increasing pressure.[/li]
[li]For compressible flow an increase in cross sectional area causes the shock wave to expand and allow an increase in velocity at a constant pressure.[/li]
[/ul]
Mathematically, mass flow rate is volume flow rate times density. Volume flow rate is a function of area and velocity (assuming the discharge coefficient is constant):
[ul]
[li]Above about Mach 0.6, velocity is a function of temperature, without a pressure component. Density is a function of both temperature and pressure, so at a constant temperature, mass flow rate is a linear function of pressure.[/li]
[li]At lower velocities, the velocity is a function of the volume flow rate at actual conditions which has a term that is the difference of the square of the upstream pressure minus the square of the downstream pressure. With everything except upstream pressure held constant (the friction factor is not constant, but is pretty close for small changes in upstream pressure) then the mass flow rate term will approximate a parabola (but will deviate because of subtracting the downstream pressure and the changes in the friction factor).[/li]
[/ul]
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
This effect is vividly evident in a diverging nozzle:
[ul]
[li]For incompressible flow (i.e., velocity below about 0.6 M), an increase in cross sectional area causes a decrease in velocity at an increasing pressure.[/li]
[li]For compressible flow an increase in cross sectional area causes the shock wave to expand and allow an increase in velocity at a constant pressure.[/li]
[/ul]
Mathematically, mass flow rate is volume flow rate times density. Volume flow rate is a function of area and velocity (assuming the discharge coefficient is constant):
[ul]
[li]Above about Mach 0.6, velocity is a function of temperature, without a pressure component. Density is a function of both temperature and pressure, so at a constant temperature, mass flow rate is a linear function of pressure.[/li]
[li]At lower velocities, the velocity is a function of the volume flow rate at actual conditions which has a term that is the difference of the square of the upstream pressure minus the square of the downstream pressure. With everything except upstream pressure held constant (the friction factor is not constant, but is pretty close for small changes in upstream pressure) then the mass flow rate term will approximate a parabola (but will deviate because of subtracting the downstream pressure and the changes in the friction factor).[/li]
[/ul]
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
LittleInch,
I've attached a slide from my 5-day class that shows what he's talking about. This is a plot of the the flow through a hole when supply is shut off. Above choked pressure the mass flow rate is linear. Below some value less than Mach 1.0 (based on dynamic pressure changes with velocity I use 0.6 Mach, others use 0.3 Mach), the flow matches the isothermal gas flow equation. The straight line in the transsonic region is simply connecting the end of one curve with the start of another. I have no idea what that flow profile looks like and from extensive research I'm pretty sure that no one else does either. I started to draw it as "S" shaped, but that implies knowledge that I simply do not have.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
I've attached a slide from my 5-day class that shows what he's talking about. This is a plot of the the flow through a hole when supply is shut off. Above choked pressure the mass flow rate is linear. Below some value less than Mach 1.0 (based on dynamic pressure changes with velocity I use 0.6 Mach, others use 0.3 Mach), the flow matches the isothermal gas flow equation. The straight line in the transsonic region is simply connecting the end of one curve with the start of another. I have no idea what that flow profile looks like and from extensive research I'm pretty sure that no one else does either. I started to draw it as "S" shaped, but that implies knowledge that I simply do not have.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
Dang I wish there was an edit feature. I plotted volume flow rate at standard conditions on the attachment to the previous post, which is a 1:1 surrogate for mass flow rate (i.e., had I plotted mass flow rate the line would have looked exactly the same).
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
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See CalumB, I assumed that this was a work project (maybe like the flow through a hole experiment I did for the graph I attached), and never considered that it was a school assignment. Now all the work I did will be deleted along with your cheating on your homework. Maybe I'll copy it into an FAQ for future non-cheating uses. I guess the next time we see you, your handle will be CalumC, I hope you are more discrete in your next iteration.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
- Thread starter
- #13
JammyHam,
It used to be that any student post got the student removed from the site. Recently the site management has implemented a don't ask/don't tell policy. When you posted your question, there was a reasonable chance it was work related and I didn't ask. When you posted scans of your text book there stopped being any chance of ignoring the fact that this was homework.
There is a lot for someone to learn on this site, mostly that there is a point in your career where things suddenly stop being black and white and you find there are so many subtle shades of gray. The white-hairs on this site are mostly guys who are regularly asked to differentiate really light gray from slightly darker gray. And we argue a lot about the nuances of those seemingly tiny differences. Probably very little that can help with school work (mores the pity), but a ton of stuff to help with a career.
I'm sure someone will come across your uploaded files and ask site management to delete the thread. When it happens just go with the flow and don't post homework questions again. Ask questions and participate in the discussion, but don't post "please explain the equation on page 67 of my book" kind of questions ever again. Nothing to apologize to me about, just learn the rules and abide by them.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
It used to be that any student post got the student removed from the site. Recently the site management has implemented a don't ask/don't tell policy. When you posted your question, there was a reasonable chance it was work related and I didn't ask. When you posted scans of your text book there stopped being any chance of ignoring the fact that this was homework.
There is a lot for someone to learn on this site, mostly that there is a point in your career where things suddenly stop being black and white and you find there are so many subtle shades of gray. The white-hairs on this site are mostly guys who are regularly asked to differentiate really light gray from slightly darker gray. And we argue a lot about the nuances of those seemingly tiny differences. Probably very little that can help with school work (mores the pity), but a ton of stuff to help with a career.
I'm sure someone will come across your uploaded files and ask site management to delete the thread. When it happens just go with the flow and don't post homework questions again. Ask questions and participate in the discussion, but don't post "please explain the equation on page 67 of my book" kind of questions ever again. Nothing to apologize to me about, just learn the rules and abide by them.
David Simpson, PE
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
- Thread starter
- #15
Thanks for your help anyway - you seem like a genuinely good man. I have to admit though, cannot get my head round it - I understand that we should look things up in books but I must have looked in about 20 now with nothing. My lecturers have been no help - I guess the hunt continues.
Good luck with "whatever you do", sorry to sound rude there - just dont know your occupation or life. Again, I am sorry for how this turned out - it wasnt my intention. I just needed help with explaining why my results had that change. Sorry.
Good luck with "whatever you do", sorry to sound rude there - just dont know your occupation or life. Again, I am sorry for how this turned out - it wasnt my intention. I just needed help with explaining why my results had that change. Sorry.
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