Why does resistance change in fluid flow from laminar to turbulent conditions?

[SBMDStudent]

I was hoping someone could give me an explanation as to why resistance of a fluid moving through a tube changes from being determined by viscosity in conditions of laminar flow to being determined by density in conditions of turbulent flow.
Thanks in advance.

 

[jedishrfu]

perhaps this article from wikipedia will help:

http://en.wikipedia.org/wiki/Laminar_flow

and for turbulent flow:

http://en.wikipedia.org/wiki/Turbulence

laminar flow makes certain assumptions about the fluid that aren't true when the flow increases beyond a certain point. These assumptions help to minimize some terms in the Navier Stokes equation which describes all types of flows and makes it possible to solve for it for the simpler laminar flow.

Lastly, Navier-Stokes:

http://en.wikipedia.org/wiki/Navier-Stokes_equations

 

[Chestermiller]

I was hoping someone could give me an explanation as to why resistance of a fluid moving through a tube changes from being determined by viscosity in conditions of laminar flow to being determined by density in conditions of turbulent flow.
Thanks in advance.

Hi SBMDStudent. Welcome to Physics Forums.

In turbulent flow, the local fluid velocity vector is time dependent, and has rapidly fluctuating components in all directions. Parcels of fluid cross the mean streamlines in both directions, and carry momentum across the streamlines. So parcels from faster moving regions cross into slower moving regions, and vice versa. The net result is transport of momentum perpendicular to the streamlines, over and above that from viscous shear. This translates into higher flow resistance. See Transport Phenomena by Bird, Stewart, and Lightfoot.

Chet

 

[SBMDStudent]

Thank you for the help. I don't have much in the way of physics information to offer back, but I'm happy to answer anything in the area of medicine.

 

[boneh3ad]

In the entry region where the flow is laminar, the pressure drop (or flow resistance if that is what you prefer to call it) should depend on more than just the viscosity. In fact, you can get the pressure drop exactly in the laminar case (subject to several assumptions) using the Hagen-Poiseuille equation, which shows that the pressure drop is actually related to the viscosity, the flow rate and the size of the tube, not just the viscosity.

When the flow transitions to turbulence, as mentioned before, there is a lot of mixing involved and this tends to create a more highly curved velocity profile than the laminar case. Since the flow resistance is related to the velocity gradient at the walls, a turbulent flow will have a greater pressure drop than an equivalent laminar boundary layer. Still, it will not only depend on density in general. It will have similar dependencies to the laminar case, though with different relationships between parameters.

It sounds to me like whatever source you are getting this from is making some additional assumptions or applying a special case. What exactly does it say about this topic?

 

[Chestermiller]

When the flow transitions to turbulence, as mentioned before, there is a lot of mixing involved and this tends to create a more highly curved velocity profile than the laminar case. Since the flow resistance is related to the velocity gradient at the walls, a turbulent flow will have a greater pressure drop than an equivalent laminar boundary layer. Still, it will not only depend on density in general. It will have similar dependencies to the laminar case, though with different relationships between parameters.

Actually, for turbulent flow in a tube, the mean axial velocity profile is flatter than in laminar flow near the center of the tube and steeper near the wall. See BSL Transport Phenomena. Because of the turbulent mixing involved away from the wall, the eddy viscosity away from the wall is much higher than the actual shear viscosity of the fluid. This causes the velocity profile to be flatter away from the wall. Near the wall, in the laminar sub-layer, the turbulent fluctuations are surpressed, and the shear rate is higher than in laminar flow.

Chet

 

[boneh3ad]

All of which is supported by what I just said, particularly in light of the fact that the wall shear stress that gives rise to pressure drop is dependent on the wall-normal velocity gradient at the wall.

 

[Chestermiller]

All of which is supported by what I just said, particularly in light of the fact that the wall shear stress that gives rise to pressure drop is dependent on the wall-normal velocity gradient at the wall.

It think we are in total agreement. The only thing I was really questioning was the statement the velocity profile in turbulent flow is more curved than in laminar flow. I wanted to clarify that it is actually flatter in the central region of the flow.

 

[boneh3ad]

It is more sharply curved where it counts, near the wall.

 

[Chestermiller]

It is more sharply curved where it counts, near the wall.

Agreed (again). I was strictly endeavoring to be more precise and avoid confusion for those new to this material.