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At what Reynolds number, can viscoisty of water be ignored in an open channle flow. 

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September 23, 2015, 01:55 
At what Reynolds number, can viscoisty of water be ignored in an open channle flow.

#1 
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hi,
is there any particular value of Reynolds number, where the viscosity of water can be ignored. Like i know that in turbulent flow, viscosity effect is less, and this is what distinguishes turbulent flow from laminar flow; but someone told me that for Re > 10k, viscosity can be ignored. However, i cannot find any source. So can anyone confirm this, or cite some published paper, or anything like that. I am considering open channel flow here. Thanks a lot. 

September 23, 2015, 03:21 

#2  
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Filippo Maria Denaro
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Using the Euler equations (zero viscosity assumption) in channel flows is actually a very bad assumption...what do you want to simulate? 

September 23, 2015, 04:12 

#3 
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i am not particularly looking into any simulation.
i was just doing some dimensional analysis (buckingham's pi theorem and all), and had the dynamic viscosity term. i want to get rid of this viscous term, and someone told me that it can be ignored if reynolds number is > 10k. so i want to confirm this thing if this is indeed true, and if there is any published paper saying the same. 

September 23, 2015, 04:25 

#4  
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Filippo Maria Denaro
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It is well known from the old Prandtl theory that very low viscous flows can be treated as inviscid everywhere except from a small bounday layer near to a wall where viscous forces are always relevant. 

September 23, 2015, 04:30 

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ya, i guess i will look into the prandtl theory then, to get a definitive value of such a limiting reynolds number, if any such thing exists. thanks :)


September 23, 2015, 04:35 

#6  
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Filippo Maria Denaro
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No, for flow over a wall, the boundary layer thickness diminuishes as the viscosity diminuishes but it still exist. Using the inviscid hypothesis (Euler equation) leads to unphysical stress analysis on the wall. A classical field is the aerodynamics where wing section studied with potential flows leads to acceptable solution for the pressure distribution but the viscous corrections are then necessary 

September 23, 2015, 04:41 

#7 
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okay, so i guess there will be viscous effects close to the wall even when turbulence is high and viscosity is low (in case of air) but away from the wall, i can ignore the viscous term, right?
edit: i guess i can ignore the viscous term outside the viscous sublayer..which is generally thin in case of high reynolds number. 

September 23, 2015, 06:45 

#8  
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Filippo Maria Denaro
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be carefull, in confined flow is somehow arbitrary a subdivision in internal (viscous) and external (inviscid) flow conditions...It strongly depends on what you are looking for... 

September 23, 2015, 06:50 

#9 
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oh i see, will look into that..
thanks for all your replies :) :) 

September 23, 2015, 07:01 

#10 
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Viscosity can be ignored, which gives you an Euler equation, when you want to examine farfield effects. If you have a wallbounded flow and specifically want to look at the nearfield region then viscosity can never be ignored.
As Reynolds number increases, the influence of viscosity decreases, however the velocity gradients increases. In the case of infinite Reynolds number where viscosity influence tends to 0 the gradients tends towards infinity so that the dissipation rate tends towards a constant. Actually this is analogous to criticality phenomenon and viscosity is only ever zero at the critical point, which mathematically happens to be infinite Reynolds number. Last edited by LuckyTran; September 24, 2015 at 14:18. 

September 23, 2015, 07:42 

#11  
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can u check the words in bold and confirm if u mean that: when Re tends to infinity, velocity gradient tends to infinity or zero? i didnt get it completely.. 

September 23, 2015, 09:08 

#12 
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Filippo Maria Denaro
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the Re number can be written as (U/L) * L^2/ni, U/L is homogeneous to the gradient of the velocity.
Re> inf can be due to ni>0 for finite U/L, or U/L> inf for finite value of ni. 

September 24, 2015, 09:19 

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oh i see, thanks for the answer :)


September 24, 2015, 14:20 

#14 
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Lucky
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sorry velocity gradient increases with Reynolds number. I fixed it now.


Tags 
open channel flow, reynolds number, viscosity 
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