# Poiseuille flow for Rectangular Annulus

 Register Blogs Members List Search Today's Posts Mark Forums Read

 May 11, 2011, 01:01 Poiseuille flow for Rectangular Annulus #1 New Member   arunima Join Date: Oct 2009 Posts: 4 Rep Power: 10 Hello All, Has anybody derived equation for pressure drop or flow rate for flow through rectangular annulus (hollow rectangular section). Please let me know any literature available on this. Thanks for your help.

 May 11, 2011, 01:52 #2 Super Moderator   Oliver Gloth Join Date: Mar 2009 Location: Todtnau, Germany Posts: 117 Rep Power: 10 Hi, if the flow is turbulent you can use the relations for circular ducts and replace the diameter with the hydraulic diameter Dh = 4*A/P (A: cross section, P: perimeter). For laminar flow you can find an analytical solution in VISCOUS FLUID FLOW by Frank M. White (eq. 3-48 on page 113). Cheers, Oliver

 May 11, 2011, 05:57 Re: Poiseuille flow for Rectangular Annulus #3 New Member   arunima Join Date: Oct 2009 Posts: 4 Rep Power: 10 Thanks Oliver for quick response, The flow is highly viscous(laminar). I am refering second edition "VISCOUS FLUID FLOW" by Frank M. White. In my book, the analytical solution for rectangular section is given (eq. 3-48 on page 120). Does new edition give solution for hollow rectangular flow? Can you please forward the solution to my mail-id arunimamukherjee1989@gmail.com. I was thinking velocity profile be integrated twice to give flow rate. First along z-direction, a1 to a2 second along y-direction, b1 to b2 considering symmetry along y-axis and z-axis. But stuck what should "a" & "b" be in the formula. like should be max or min.(a1 or a2). Please help.

 May 11, 2011, 06:10 #4 Super Moderator   Oliver Gloth Join Date: Mar 2009 Location: Todtnau, Germany Posts: 117 Rep Power: 10 Can you please clarify what you mean with "hollow rectangular flow"? I thought it was the flow through a rectangular pipe -- i.e. exactly what eq. 3-48 describes. Btw. I have edition 3, but I assume it is the same formula. In my book the flowrate Q is given as a function of the pressure gradient. I'll scan the page and send it to you.

May 11, 2011, 06:42
#5
New Member

arunima
Join Date: Oct 2009
Posts: 4
Rep Power: 10
Hello Oliver,

I am looking for flow rate or pressure drop equation for Hollow Rectangular Section means something like rectangular annulus. I have attached the photo of my domain. Please find the same. Can you please help me in deriving the equation for flow for this type of section. Is my methodology right which I posted earlier.

Thanks
Attached Images
 Hollow Rectangular.jpg (82.2 KB, 13 views)

 May 11, 2011, 08:23 #6 Super Moderator   Oliver Gloth Join Date: Mar 2009 Location: Todtnau, Germany Posts: 117 Rep Power: 10 my fault -- should have read your original post more carefully. It depends a bit on what is your objective; if you absolutely need an analytical formulation it will be quite difficult I guess. Otherwise you can try the hydraulic diameter approach. As a start you can take a circular annulus for which you have an analytical solution in the book. Then compare that solution with the hydraulic diameter approach and decide if the error is acceptable for you or not.

 May 11, 2011, 10:43 #7 New Member   arunima Join Date: Oct 2009 Posts: 4 Rep Power: 10 Hello Oliver, Even from my side there was data loss during communicating. Actually I need to calculate pressure drop throughout our product. I have formulas for other section, whereas for this section I find none. My section is similar to *.jpg file. I need to read hydraulic diameter concept. I would calculate error and update you. In between if I have any doubts I would ask you. Please help. Hearty thanks for your kind support.

 May 18, 2016, 02:48 rectangular annular #8 New Member   jenan Join Date: May 2016 Posts: 1 Rep Power: 0 Hello every body I need to know how can I make a discretization fod the Governing differntial equation using FDM with marching technique for fully developed viscous flow inside rectangular annular

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post kevin FLUENT 8 August 11, 2015 13:00 alberto OpenFOAM Running, Solving & CFD 0 December 3, 2009 03:03 saii CFX 2 September 18, 2009 08:07 Zhihua Xie CFX 0 September 3, 2007 09:49 pxyz Main CFD Forum 37 July 7, 2006 08:42

All times are GMT -4. The time now is 07:50.