If I understand your question correctly (which is not a 100% certain), the entrance length for _laminar_ flow (x_FD -- i.e the downstream distance at which the flow becomes fully developed, and therefore becomes independent of any entrance effects) is given by the following relationship (which can be found in most engineering-oriented fluid dynamics textbooks):

x_FD / D_h = 0.06*Re

where D_h = 4 * A_cs / P - hydraulic diameter (where A_Cs is the channel cross-sectional area and P is the so-called "wetted perimeter"),

and where Re = U_av * D_h / nu (where U_av is the average streamwise fluid velocity = mass flow rate divide by the density * A_cs) and nu is the kinematic viscosity of the fluid.

As for the distance from the exit, that question, to my knowledge, has been less widely studied...

This being said, there are analytical solutions for laminar flow in fully-developed channels of circular or rectangular cross-section.

Best wishes,

LM

Analytically ,the entrance length for the fully developed channel flow is calculated using the formula (Le/D) = 0.05Re. Where Le = Entrance length. D=Hydraulic dia/2.

Best wishes

One way to avoid the influence from the outflow boundary, is to implement a special 'no-inflow' kind of boundary condition.  Instead of simply extrapolating across the boundary, put in a condition that sets the velocity perpendicular to the boundary to zero  if there is any motion back into the channel. Something like

v(n+1) = max(v(n), zero))

with v the velocity along the pipe, n the last gridcell inside the computation grid and n+1 the first cell in the boundary. This way you prevent a signal from travelling back upstream from the boundary.

This method works well in astrophysical problems. It may work for your application as well.

Dear Settar,

Your job is physical experiment? Or, computational work?

Thanks for you interest dear Ji Ryong Cho, 

My work is physical experiment. I have to approach a uniform temperature at a metallic surface, to release the heat flux using this cold water circulation.

Oops, sorry. I'm so used to doing numerical simulations, that I automatically think in those terms. Obviously, my solution is not going to work in real life.

Dear Settar,

Design consideration on the inlet entry zone is suggested above by others. Installation of fine grid at the outlet is helpful in reducing upwards propagation of outside disturbance (for example, pressure fluctuation due to room draught).  Regards, Ji.      

To add to Ji Ryong Cho's useful comment, a (low-blockage-ratio) honeycomb installed at the exit of the tunnel / channel has also been used in wind tunnel designs to minimize outside effects from being communicated upstream into the test section.

Thanks for all your answers.

I think that's essential to make the channel long enough to reach the fully developed flow in the test section.