Laminar and Turbulent Flow

[LR89]

Why does laminar flow occur at low velocities and turbulent flow occur at high velocities? I'm trying to understand it in terms of flow over a cylinder and adverse pressure gradients but I can't understand why an object moving at a higher velocity would experience a greater adverse pressure gradient than one moving at a slower velocity. Thank you!

[Bignose]

It is the instability of flow that causes turbulence. There is a whole study of fluid mechanics on stability. In short, viscous dissipation is not enough to dampen certain disturbances. Check out the absolute classic by Drazin and Reed, Hydronamic Stability They just put out a 2nd edition not too long ago. I have the first edition, and it is still the first place I consult on stability issues. There are more advanced texts out there, but this is an excellent starting point.

[cypress]

Laminar flow occurs at low velocity where total kinetic energy is lower and less is available to contribute to fluid "sheer" due primarily to fluid viscosity near the solid boundaries. Laminar flow is characterized by low convection of momentum perpendicular to flow as the flow remains largely in smooth sheets with relatively high friction from one sheet to the next. Thus the flow profile has extended distribution perpendicular to flow, and the ratio of resistance to flow vs. total energy is greater and thus a greater percentage of momentum is consumed by frictional losses. In laminar flow fluid sheer is consistent, steady and smooth but as velocity rises the sheer becomes chaotic as the energy gradient is partially able to overcome kinematic viscosity and momentum flows convectively much further into the boundary layer disrupting the laminar sheets and reducing the ratio of friction losses to total energy.

 

The adverse pressure gradient is a related issue as it is a boundary layer phenomena. Boundary layers are established for solid object traveling through fluids. The solid object acquires a boundary layer subject to the same viscus forces discussed previously. As geometry imposes more severe perpendicular flow requirements relative to undisturbed potential flow, dead spots result in kinetic energy converted to potential energy causing adverse pressure gradients.

 

It is not that turbulent flow in boundary layers experience adverse pressure gradients rather it is that they are able to better sustain them without causing boundary layer separation and thus eddies. This is because the convective transfer of momentum in turbulent flow boundary layers provides more energy to sustain the adverse pressure gradient before separation occurs.

Edited September 21, 2010 by cypress

[CaptainPanic]

Turbulent flow causes a lot of internal "friction" inside the fluid (shear stress is a better word though), which means that a lot of energy is lost in creating heat. Logically, that energy has to come from somewhere, and that somewhere is the greater pressure drop and thus the greater energy needed to push the fluid through the pipe.