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rashmi May 11, 2011 01:01

Poiseuille flow for Rectangular Annulus
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.

ogloth May 11, 2011 01:52


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).


rashmi May 11, 2011 05:57

Re: Poiseuille flow for Rectangular Annulus
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

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.

ogloth May 11, 2011 06:10

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.

rashmi May 11, 2011 06:42

1 Attachment(s)
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.


ogloth May 11, 2011 08:23

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.

rashmi May 11, 2011 10:43

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.

jenan May 18, 2016 02:48

rectangular annular
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

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