Jump to content



Featured Articles

Check out the latest featured articles.

File Library

Check out the latest downloads available in the File Library.

New Article

Product Viscosity vs. Shear

Featured File

Vertical Tank Selection

New Blog Entry

Low Flow in Pipes- posted in Ankur's blog

Calculating Pressure Vs. Time While Filling Tank


This topic has been archived. This means that you cannot reply to this topic.
11 replies to this topic
Share this topic:
| More

#1 Hankj

Hankj

    Brand New Member

  • Members
  • 7 posts

Posted 29 April 2014 - 03:23 PM

Hello,

 

First off, this is my first time posting. However, I have browsed these forums quite a bit in the past. I am a undergrad student currently on a co-op term. 

 

I need to generate a graph showing the pressure of a tank vs. time. I will have a large tank pressurized, with air, at P1 connected to a smaller tank with piping of a known area A. The larger tank will be much larger than the smaller tank, therefore, we can assume the large tank will stay at P1. The smaller tank has a volume of Vt

 

This question is almost identical to this question from the past: http://www.cheresour...-vesselstorage/

 

However, I do not feel like the question was fully answered in that post. The equation that the poster was working with is:

 

ρair*v*A = [Vt*MWair/(ZRT)]*d(P-P1)/dt

 

Like the original poster, I am confused on how to calculate the velocity (v) and I understand that it changes as the pressure differential between the two tanks changes. 

 

Thanks so much in advance!


Edited by Hankj, 30 April 2014 - 09:24 AM.


#2 Neelakantan

Neelakantan

    Gold Member

  • Members
  • 124 posts

Posted 01 May 2014 - 06:35 AM

 I have not seen the post that you have referred so I cannot answer that; but I can give a general idea how I would go about doing it:

 

1) you have a source (you say it is constant pressure and large) ; you are connecting a smaller tank and pressurizing it; imagine a situation where an (ideal) air compressor is discharging into a cylinder; the compressor is capable of discharging large quantum; so the limitation on filling is the connection resistance; (also remember it is not steady-state, the cylinder is getting filled with differential rate; that is why you are asked to draw a graph against time!)

2) you mentioned the smaller tank is connected by a pipe/tube of known area; you also need to know the (equivalent) length so that you can know the overall resistance to flow in the connection; knowing the pressure difference and the resistance we can calculate flow at any instant

2b) you can have a situation where the resistance is not  determining factor; that is choke-flow; look up choke-flow  or mach number to understand where such a situation happens; in your problem it would be case initially (hint: as long as the tank pressure is half the source the flow could be choke-flow!)

3) at any instant, given the pressure difference, the flow is determined;  you are dealing with a compressible fluid; and the basic equation is known (I presume you know; and remember, this is a steady state equation!)

3a) in your case, where the flow is not constant, the equation is a differential equation and time dependent!  if you want a mathematical equation, expressing flow, then a differential equation is to be generated

3b) your exercise is to generate a graph ( 3a above gives the flow rate, which you can convert into volume discharged and hence the pressure of the destination cylinder!)

 

Since it is a student forum, I am not giving out the answers or a graph; (look at this : http://www.lmnoeng.c...ow/weymouth.htm and also http://www.lmnoeng.com/Gas/choke.htm )  if you still fail to get it, come back, I trust our members may help and guide you to create a simple xl file to generate the graph; !

 

best wishes

neelakantan


Edited by Neelakantan, 01 May 2014 - 06:39 AM.


#3 Hankj

Hankj

    Brand New Member

  • Members
  • 7 posts

Posted 01 May 2014 - 09:39 AM

I've started to go down a different road. Instead of finding a differential equation I was trying to integrate in Excel. I was using the Poiseuille equation for a compressible fluid. I have the right information to use that equation. However, I do not know if that equation gives me a STANDARD volumetric flowrate or the absolute flow rate of gas. I'm guessing its absolute flow rate, is that correct?

 

http://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation#Poiseuille.27s_equation_for_compressible_fluids 



#4 Art Montemayor

Art Montemayor

    Gold Member

  • Admin
  • 5,780 posts

Posted 01 May 2014 - 10:36 AM

Hankj:

 

First off, I agree with the advice neelakantan is offering you.  As a student, you may not realize it now, but it is essential as an engineer to specifically identify the nature and type of problem you have in front of you.  You are differentially filling a vessel (the smaller tank) --- but only if you are flowing your gas sub-sonically.  You must obey the law of compressible fluids regarding sonic flow.  The only way you can justify avoiding sonic flow is to state that the pressure in the large vessel is such that it will not cause sonic (“choked”, “critical”) flow.  Sonic flow occurs when the ratio of the source gas pressure to the downstream ambient atmospheric pressure is equal to or greater than [(k + 1) / 2] k / (k – 1).  If your initial small vessel is at atmospheric pressure, for example, the pressure in the large vessel must be less than 28 psia (13 psig).  You must accept that as your basis if you mean to apply subsonic equations to your flow model.  For a clear and detailed explanation of this topic, please read and study the excellent attached document by Milton Beychok.

 

I believe that the Poiseuille equation that you refer to is for isothermal flow and subsonic condition.  Again, if you intend to apply an equation to a problem, you must qualify it by defining the conditions under which you apply it, making sure that it fulfills your conditions.

Attached File  Choked Gas Flow -Milton Beychok.doc   167KB   100 downloads



#5 Hankj

Hankj

    Brand New Member

  • Members
  • 7 posts

Posted 01 May 2014 - 12:23 PM

Thanks Art,

 

I hope you can clarify a few things for me. I have created a spreadsheet using only the Poiseuille equation. However, I believe I need to tweak it to comply with the choked flow. 

 

From the attachment it says: "which means that choked velocity usually occurs when the absolute upstream pressure is at least 1.7 to 1.9 times as high as the absolute downstream pressure."

 

That means if my larger vessel is at 60 psi and my smaller vessel is at 14.7 psi I need to use the choked flow equation for volumetric flow but when I reach the point where the upstream pressure is less than 1.7 to 1.9 times the smaller vessel then I use the Poiseuille equation?

 

Furthermore, the equation for choked flow contains Z, the compressibility factor at given T and P, and ρ, the density at given T and P. When calculating Z and ρ would I use the pressure of the upstream or of the downstream? 

 

Finally, is the equation for density from the ideal gas law "good enough" to use in this situation. The equation being:

 

ρair      P     

           Rair * T

 

Where, P = Pressure, ρ = density, Rair = Specific gas constant for air and T = temperature.


Edited by Hankj, 01 May 2014 - 12:43 PM.


#6 Art Montemayor

Art Montemayor

    Gold Member

  • Admin
  • 5,780 posts

Posted 01 May 2014 - 03:06 PM

Hankj:

 

Why do you continue with the Poiseuille equation when you know (or should know) its limitations?

Have you considered that you have a sonic flow condition?  Do you agree that you have sonic flow established?

 

Have you read and studied: http://en.wikipedia....iki/Choked_flow ?

Are you familiar with sonic flow?

Have you considered your own basis of design?  You stated that your source pressure is constant (and higher that that downstream).  The Poiseuille equation limits you to 0.4 Mach.  Are you below that value?

What, specifically, are your basic data?  Gas? pressures? flowrates? temperatures? volumes? pipe sizes and lengths?



#7 Hankj

Hankj

    Brand New Member

  • Members
  • 7 posts

Posted 01 May 2014 - 04:01 PM

 

 

Why do you continue with the Poiseuille equation when you know (or should know) its limitations?

It's the only thing I had when I first designed the spreadsheet.

 

 

 

What, specifically, are your basic data?  Gas? pressures? flowrates? temperatures? volumes? pipe sizes and lengths? 

Gas = Air

Large tank pressure = 60 psia

Flowrate = What I'm trying to determine

Temperature = 72 F

Volume of smaller tank = 4 cubic feet

Pipe radius =  1 inch

Pipe length = 25 ft.

 

All of this is relatively unimportant because they are going to be variables. I understand I need to use multiple equations to describe the flow. 

 

If you use the choked formula for Mach 1 and you can use Poiseuille equation only below Mach .4, what equation do you use between Mach 1 and Mach .4?



#8 Neelakantan

Neelakantan

    Gold Member

  • Members
  • 124 posts

Posted 03 May 2014 - 03:45 AM

@hankj

.

yes; you have to check the flow regime (choked flow or subsonic) before deciding the formulat you use; if you have read the link i posted you would not have perhaps asked the question about density

 

====quote from http://www.lmnoeng.c...ow/weymouth.htm

"Introduction
The Weymouth, Panhandle A, and Panhandle B equations were developed to simulate compressible gas flow in long pipelines.  The Weymouth is the oldest and most common of the three. It was developed in 1912. The Panhandle A was developed in the 1940s and Panhandle B in 1956 (GPSA, 1998). The equations were developed from the fundamental energy equation for compressible flow, but each has a special representation of the friction factor to allow the equations to be solved analytically. The Weymouth equation is the most common of the three - probably because it has been around the longest. The equations were developed for turbulent flow in long pipelines. For low flows, low pressures, or short pipes, they may not be applicable.

 

If the pressure drop in a pipeline is less than 40% of P1, then our Darcy-Weisbach incompressible flow calculation may be more accurate than the Weymouth or Panhandles for a short pipe or low flow.  The Darcy-Weisbach incompressible method is valid for any flowrate, diameter, and pipe length, but does not account for gas compressibility.  Crane (1988) states that if the pressure drop is less than 10% of P1 and you use an incompressible model, then the gas density should be based on either the upstream or the downstream conditions.  If the pressure drop is between 10% and 40%, then the density used in an incompressible flow method should be based on the average of the upstream and downstream conditions.  If the pressure drop exceeds 40% of P1, then use a compressible model, like the Weymouth, Panhandle A, or Panhandle B. You can always run all models and compare the results."

===========================

 

 if you show your excel sheet and point out the difficulties you face in developing, definitely Art or other very senior members would help you; but as mentioned by Art, first read the article he pointed out.

 

Regards

neelakantan



#9 breizh

breizh

    Gold Member

  • Admin
  • 6,292 posts

Posted 03 May 2014 - 05:18 AM

Consider this link to support your work :http://www.engsoft.c...team_flow_e.htm

 

Good luck

Breizh



#10 Neelakantan

Neelakantan

    Gold Member

  • Members
  • 124 posts

Posted 12 August 2015 - 09:15 AM

hello @smitha n

 

do provide the engineering details of the  problem  causing "deep" trouble; no information  --> no solution! bad information --> garbage solution!

neelakantan



#11 Art Montemayor

Art Montemayor

    Gold Member

  • Admin
  • 5,780 posts

Posted 12 August 2015 - 11:23 AM

smitha n:

 

This thread is over a year old.  It was started by another member and belongs to him/her.  It will be blocked in a couple of months, after it is 1.5 years old and put into archives.

 

If you are not the same OP, then you are skyjacking another member's thread for your use.

Stop this unapproved practice and start your own, new thread.  I will delete these postings of yours in this thread after a couple of days, so start a new thread with ALL the basic information as indicated by Neelakantan and outlined in this thread.

 

Thank you.



#12 smitha n

smitha n

    Brand New Member

  • Members
  • 3 posts

Posted 12 August 2015 - 11:11 PM

A large tank with pressurized air at P0 connected to a smaller tank  with piping of a known area A. the smaller tank will be at atmospheric pressure . The larger tank will be much larger than the smaller tank, therefore, we can assume the large tank will stay at P0. The smaller tank has a volume of Vt.

 

As the pressurized air fills the smaller tank its pressure goes on increasing, till pressure in smaller tank = larger tank pressure.

 

initially the flow will be choked till tank pressure pt exceeds the p*(criticalpressure);  p*=0.528p0 ( as per the theory of choked flow).

 

 

Therefore the mass flow rate will be :

 

 

93c44e9322f561d4fd5c946af9381327.png and mass flow = volumetric flow*density

 

 

Later this flow will be followed by subsonic flow (i.e. flow is not constant .The flow will depend on pressure difference and resistance by  POISEUILLE'S LAW)..

 

 

 

 

7b96206652c9910bf03abbb914fe06be.png

 

here the flow will continuously vary.now i need an equation relating pressure variation in small tank with time t. please guide to arrive the final solution.






Similar Topics