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Entrance region pipe flow

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Jan25-10, 10:25 AM
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1. The problem statement, all variables and given/known data
Two dimensional, incompressible flow with constant properties in entry region of a horizontal pipe. Assume no swirl, neglect heat transfer.
Determine governing equations.

Question is: what are the properties of the entrance region of a pipe as far as flow is concerned? It is not yet fully developed so it can't be considered parallel (poiseuille flow). The flow has irrotational core flow and the boundary layer is developing. Are there any simplifications that can be made because of this or was the entrance region specified to indicate that simplifications cannot be made?

2. Relevant equations
Incompressible Navier Stokes and Continuity equation in cylindrical coordinates

3. The attempt at a solution
2D = no partial theta terms
no swirl = no u(theta) terms
incompressible = neglect material derivative (for continuity)
no gravity in x

I have simplified the continuity equation and the theta momentum (all terms = 0). I'm just trying to figure out if there are any further simplifications that can be made to the r and x equations because of the entrance region to the momentum equations - for example: can it be considered as axisymmetric irrotational flow?
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