Mostly  50 times the diameter gives good results in most applications where flow geometries change. Although different researchers take any value from 10 D to 100 D, depending how flow development length is defined.

Newtonian fluid or non newtonian fluid?

Laminar or turbulent

Newtonian fluid and turbulent flow

Mostly  50 times the diameter gives good results in most applications where flow geometries change. Although different researchers take any value from 10 D to 100 D, depending how flow development length is defined.

Thank you for your answer

Is there any paper for reference?

Distance of about 60 pipe diameter 'd' from intake of pipe is generally considered. According to L.Schller , l= 0.03 d x Re. 

Ref: Applied Mathemaical Sciences by  Lawrence Sirovich.

Prof. Rakesh Mishra gave correct answer. 

Sadgeh,

For your application, there is a good book, internal flows by D.S.Miller. This book has details about effects of fixtures and fittings on the flow.

I am not an expert in turbulent flow.

Read these papers, useful perhap.

Hello,

Depending on the Reynolds Number, 30 to 60 times the characteristic length could be a good aproximation.

We it could use a solution brought near for: From energy equation get hr=(V1-V2)^2)/(2g) it know (Borda equiation). After x=(D2/f2)((A2/A1-1)^2)

Prof. Mishra, thanks for the guide you gave me.But I don't access to download this book. Have you this book?

Find attached some chapters of this book

find attached  another chapter

This distance is a function of the Re number. There are several semi-empirical relations in the literature. These expressions are expressed in function of adimensional parameters like Re and L/D being D the diameter for pipes and L the distance from the inlet. These relations are obtained applying Pi theorem of buckingham and experiemental measurements. You could obtain L if you know the Re number and the diameter of the pipe. For non-circular sections pipes, you must use the hydraulic diameter.

As stressed by Miguel Coussirat the development length depends on the Reynolds number. For laminar flows it is inversely proportional to the Reynolds numbers. For turbulent flows (Re>2300) the distance needed depends on the definition of "fully developed". For many applications a distance of 20 diameters can be sufficient. A distance of 50 diameters s safe if there is no longitudinal swirl in the flow. Sch a swirl can occur if there are two successive orthogonal bends in the upstream system (or another asymmetry). In case it is very important to have a fully developed flow after a reasonably short distance, you should use a perforated plate. Specially designed perforated plates exist, which are placed just upstream of turbine flow meters or ultrasonic flow meters.

THE RESPONSE IS DEPENDING OF THE REGIME OF THE FLOW.

A DISTANCE THAT IS EQUAL TO 5 OR 6 TIMES THE DIAMATER OF THE EXPANSION DUCT IS ENOUGH TO REACH THE FULLY DEVELOPED REGIME FLOW. 

it is not necessary to find in a research paper to read about this. In a first technical approach, this problem is a handbook's solution. You can read about developed flow length in any classical Fluid Mechanic book, e.g. White, Çengels Cimbala, Fox, etc.

Best regards

Hi Ouchiha

Firstly the distance of 5 to 10 times the diameter duct is not sufficient to reach fully developped flow. I think that   Avraham Hirschberg proposition is very reasonnable and very practice.. I tested 20 to 30 times and it gives acceptable results

The expansion angle not to exceed 9 degrees

The 9 degrees is the opening angle of a conical expansion in which one tries to avoid flow separation (Blevins, Fluid Dynamics Handbook). This is actually only valid for high Reynolds number flows (turbulent flow). It is not related to the original question: how far downstream of an abrupt expansion (with flow separation) does one recovers a fully developed flow.

In the scientific references, a distance of 20-50 diameter is recommended for fully developing of flow after sudden expansions. For the open channels, the experimental data shows that using a hump decrease the flow separation and energy loss. In this case, hump with a crest height of 5-9% of the approach depth are recommended. for more information, you can refer to this valuable paper:

http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29IR.1943-4774.0000803