Continuity equation in pipes Qin=Qout... does it apply to air/gas? 1

[USAeng]

I cant remember the answer to this question - I had more stuff in college dealing with incompressible fluids than air/gas...

I was taught qin=qout so if you have a fan blowing 200cfm air into a 6" pipe and then it reduces down to 2" then enlarges to 12" then reduces back to 2" again --> then the flow at the 2" exit is still 50cfm just at a higher velocity correct? ignoring friction losses Q=VA

This amount of air can only flow through a smaller and smaller opening to a point though right? what if you reduced the opening in the pipe to 1/2" or lower... there is no way the fan could still pass that much air through that small of an opening... so would it cause the fan to overheat or? and is there an equation to figure out how small of a round pipe could still pass that amount of air?

 

[zdas04]

First off, the continuity equation deals with mass flow not volume flow.

Second, if you took more (or less) mass from a pipe than you put in, where would the extra come from (or where did it go)?

Yes, the continuity equation applies to compressible fluids. And no, very little of you post was correct.

m(dot)=vA(rho) at every point in a pipe m(dot) is the same. At any point, q=vA, but both the velocity and the area can change nearly independently (a change in pipe size does change velocity, but a change in pressure for the same pipe size changes velocity too).

I don't even know where to start expalining what is wrong with the rest of your post.

David

 

[USAeng]

sorry I meant 200cfm not 50cfm for the second part... and your post is a little harsh in my opinion... thanks for answering anyways

 

[dcasto]

on your response, no. CFM is conserved, standard CFM is as at standard conditions, the mass is known.

so 200scfm in and 200 scfm out is correct.

 

[zdas04]

Dennis,
You were the one who addec the "S", there is nothing in the original post that even implied that he was talking about standard cubic feet. SCF is a reasonable surrogate for mass flow rate and it is conserved. ACF is neither.

David

 

[USAeng]

Sorry I obviously do not know enough about this subject... like I said I have had almost no experience with gases and I'm still young and trying to learn. I wanted to spur some discussion so that I could start learning something that is a bit work related at the moment, and I guess in your belittling (at least they came off that way) responses I did at least accomplish some of that... so anyways, I will go read more about the subjects mentioned and if anyone can point me in the direction of a book that's worth reading on the subject I would appreciate it. Next time I will just ask for the book. Thanks.

 

[zdas04]

USAEng,
I'm sorry that you took my responses to be belittling. That was not my intent. My intent was to make you understand that terms like "continuity equation" have precise mathematical definitions, and if you are going to use a term like that you should get it right. Volume flow at actual conditions is occasionally a useful concept, but it has very limited application (e.g., ACF at one pressure cannot be added to ACF at another pressure).

Mass flow rate on the other hand is a basic function and the mass flow rate at one pressure can be added to the mass flow rate at a different pressure. Mass flow rate is conserved (i.e., for a closed system with no additions or removals of mass, the mass flow rate at every point in the system is equal to the mass flow rate at every other point).

The SCF that dcasto mentioned is a reasonable surrogate for mass flow rate since at any point in the closed system SCF/time is mass flow rate divided by the same density (i.e. the pretend density that the gas would posses if it were at standard conditions).

I didn't mean to belittle you, I meant to make you understand that if you are going to use engineering terms it pays to use them with precision.

David

 

[USAeng]

OK thank you very much for responding and letting me know you had no ill intentions... and I see now where you were coming from. I look forward to learning more so I can speak in better terms.

I guess for the meantime I will try and reword my first attempt into more of what I directly need at the moment... Say if there is a fan blowing directly into a round duct and you put a restriction farther along in the duct that blocks off some given majority of the diameter - is there a diagram somewhere that shows how something like that will effect relationships of pressure, flowrate, etc?

Thanks again for getting back and sorry for the misunderstanding

 

[zdas04]

You were on the verge of the right track. Sorry, no diagram handy.

The mass flow in the big duct must equal the mass flow out the little hole. That means that the velocity has to increase a bit out the little hole. If the pressure in the duct increases to more than about 6 psig, then the flow will be "choked" (there is a good description of choked flow in the FAQs for this forum) and the air exiting out the hole will be at sonic velocity. If the upstream pressure continues to increase, then the velocity will remain at Mach 1.0, but the upstream density and therefore the mass flow rate (m=v*A*rho) will increase until you reach an equilibrium point where d(flow)/dt=0 and the continuity equation can be satisfied.

If the pressure never builds up high enough to give you choked flow (e.g., you don't have enough hp in your blower to increase the pressure to choked flow) then the basic concept still holds, but the arithmetic gets a lot messier.

David

 

[USAeng]

What is the effect of the restricter on the fan and it's input/output? After the fan's output it would be higher static pressure but lower flowrate? I assume the fan will not be sucking as much air in after the restricter reaches a certain size? I have never dealt with mach numbers or sonic anything so I am going to have to look into that more later today. I will also look up that info on the choked flow. Thanks.

 

[dcasto]

zdas, I added the s to show that a standard cfm IS continuity.

 

[gruntguru]

What is the effect of the restricter on the fan and it's input/output? After the fan's output it would be higher static pressure but lower flowrate?

Yes. The restriction will increase pressure upstream (which includes the fan discharge). This will move the operating point of the fan to a lower flowrate.

Engineering is the art of creating things you need, from things you can get.

 

[DLite30]

Bueller....Bueller....Bueller

 

[planck121]

zdas4,
Just a bit of a correction with your post

"First off, the continuity equation deals with mass flow not volume flow"

Q= V.A is also a special form of the continuity equation. Infact from M(dot) = V.A.Rho and you divide the M(dot) with density (rho) we have the volumetric flow. The original form of the volumetric continuity equation is therotically

Q= V.A Cos(theta) now when the flow is perpd to the cross sectional area of consideration we have Cos0 = 1 so we the refined form Q= V.A

I still treat this as a continiuty equation for 1D flow (incompressible). Typically I would use the intergal versions of these queations (including the mass flow) for surface/area calculations and differential versions of the equations (for point/local calculations).

Cheers

 

[zdas04]

Planck121,
As I said above, engineering terms have a precise mathematical definition.

Mass flow rate = volume flow rate * density

The continuity equation says that mass flow rate (absent additions or removal of fluid) will be equal at every point in the system.

That says that the product of volume flow rate and density must be the same at every point, not that either the volume flow rate or the density is constant. So if the pressure decreases at a constant temperature, then the volume flow rate must increase by a proportional amount. Since volume flow rate is velocity times area, if the area is constant and the volume flow rate increases, then the velocity must have increased. Nothing about this implies that volume flow rate at actual conditions is a constant. The only "special case" is the one that dcasto mentioned above--if you use an imaginary (and constant) density then the continuity equation holds for a volume flow rate at standard conditions.

I stand behind everything I said in earlier posts.

David

 

[planck121]

zdas04,
Thanks for the response. I concur with you to a point, my intial post was to try to address the fact that Q=V.A is also a continuity equation (perhaps a special form if you like to call it so), I am in agreement with what you have mentioned (interplay of charles and bolyes laws, i.e PVT drops and increases).

However lets slightly twist the senerio and see things in a different way. Assume you have restriction orifice and are modelling a flow through this orifice. The bernoulli's equation practically reduces to (P1/rho)+ V1^2/2 = P2/Rho + V2^2/2 (assuming contant height and most importantly, Incompressible flow (contant density), invisid (for all practical reasons consider it as ideal liquid neglecting viscioius effects). At that point Q1 = Q2 (volmetric flow rates will be contanst) and hence we can go onto conclude V1.A1 = V2.A2 to further simply the final equation through an orifice leading to

Q = C.A2(Sqrt 2*(P1-P2)/rho)
c being the coffiecient of discharge.
Typical equation to determine vol flow through orifice. My apologies cause I cannot seem to get the math symobls to show up the way I want them to in the txt.

Had it not been for the treating Q1 = Q2 through the orifice/restriction we would never be able to resolve the equation.

Cheers

 

[planck121]

Just as an addendum. The area when we are modelling the flow through the orifice (is not constant, i.e A1 not equal to A2), A1 being area of the pipe and A2 being the cross area of the orifice. So V1 and V2 are changing so is A1 and A2 hence Q1 will have to equal Q2 for conservation and continiuty, atleast through the orifice in this case.

 

[zdas04]

Bernoulli's equation absolutely does not allow density to change. Therefore, over the distance that the equation is valid (inches of pipeline length, maybe feet, not yards) since density is constant, volume flow rate must also be constant.

Adding a friction term to Bernoulli's equation REALLY sets me off. One of the most ham-handed bastardizations in all of engineering is the so-called "Modified Bernoulli Equation". Nothing about it makes sense from either a theoretical or operational viewpoint. I can get to the same place with Darcy Weisbach (for liquids) or AGA Fully turbulent (for gases) without violating any underlying assumption. That equation is just lazy and stupid.

The AGA 3 equations started with Bernoulli's equation and have had empirical tweeks to get to a usuable real-world result. These tweeks are based on a database of many hundreds of thousands of data points and don't claim to be anything but empirical.

David

 

[BigInch]

Are we totally sure that it is not the Betz factor that is being danced around here with this partially restricted duct affecting the fan upstream thing.

http://en.wikipedia.org/wiki/Wind_turbine_aerodynamics

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