Calculating the hydrodynamic entry length of a cicular pipe.

In summary, there are several formulae available that give a ratio of the entry length to the pipe diameter to the Reynolds number, ranging from 0.02-0.06. However, there is no known derivation for this solution and it is believed to be based on experimental data. The Boussinesq approximation from 1892 is often referenced as a classic solution for laminar flow, but finding the original derivation is difficult. There is also a need for a similar solution for 2D channel flow.
  • #1
wildturkey101
2
0
Does anyone know how to calculate the entry region length of laminar incompressible flow in a pipe? There are several formulae available which give a ratio of the (entry length)/(pipe diameter)/(Reynolds number) = 0.02-0.06.

I'm not looking for the final solution, but rather the approach used in order to calculate the entry region as a function of Reynolds number and pipe diameter, and so far have been unsuccessful.

It's a classic problem originally handled by Boussinesq, but I can't seem to find any literature sources that actually go through the derivation. All the fluids books I've looked at just give the final expression:

X_entry length = 0.05*Reynolds*Diameter.


Any help?
 
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  • #2
I don't think you're going to find a derivation for that. IIRC those are correlations from a lot of experimentation.
 
  • #3
Analytic solutions are possible, but I've just been bogged down in the mathematics...

Boussinesq first solved it analytically back in 1892 to give the classic approximation for laminar flow of (X/D)/Re=(1/20) ... No one seems so keep 19th century French fluid mechanic journals on file anymore. ;)
 
  • #4
I'm looking for the same solution for 2D channel flow. Can someone help me? I need the derivation
 

What is the purpose of calculating the hydrodynamic entry length of a circular pipe?

The hydrodynamic entry length of a circular pipe is calculated to determine the distance required for the flow to fully develop and reach a steady state. This is important for accurately predicting the flow rate and pressure drop in the pipe.

How is the hydrodynamic entry length calculated?

The hydrodynamic entry length can be calculated using a variety of methods, such as the dimensional analysis method or the empirical correlation method. These methods take into account factors such as the pipe diameter, flow velocity, and fluid properties to determine the entry length.

Why is the entry length different for different fluids?

The entry length is affected by the viscosity and density of the fluid. Viscous fluids have a longer entry length because they experience greater resistance to flow, while less viscous fluids have a shorter entry length.

What is the significance of the entry length in fluid flow calculations?

The entry length is important because it affects the accuracy of flow calculations. If the entry length is not taken into account, the flow rate and pressure drop in the pipe may be overestimated or underestimated, leading to inaccurate results.

Can the hydrodynamic entry length be reduced?

Yes, the entry length can be reduced by using flow control devices such as screens or honeycomb inserts, which disrupt the flow and allow it to develop faster. However, these devices can also increase pressure drop and should be carefully considered in the design of a system.

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