p density of fluid, kg/m3 [Greek letter rho] V mean velocity of fluid, m ...

Real_Fluid_Flowhttp://www.centennialofflight.gov/essay/Theories_of_Flight/Real_Flui...2 of 3 1/1/2011 8:33 AMd characteristic length, mµ coefficient of viscosity, kg/m-secFor this setup, Reynolds found, by using water, that below R = 2,100, the flow inthe pipe was laminar as evidenced by the distinct colored filament. This valuewas true regardless of the varying combinations of values of p, V, d, or µ. Atransition between laminar and turbulent flow occurred for Reynolds numbersbetween 2,100 and 40,000 depending upon how smooth the tube junction wasand how carefully the flow entered the tube. Above R = 40,000, the flow wasalways turbulent, as evidenced by the colored fluid filament breaking upquickly. The fact that the transition Reynolds number (between 2,100 and40,000) was variable indicates the effect that induced turbulence has on theflow.The numerical values given for the transition are for this particular experimentsince the characteristic length chosen, d, is the diameter of the pipe. For anairfoil, d would be the distance between the leading and trailing edge called thechord length. Additionally, water was used in the Reynolds experiment whereasair flows about an airfoil. Thus, the transition number between laminar andturbulent flow would be far different for the case of an airfoil. Typically, airfoilsoperate at Reynolds numbers of several million. The general trend, however, isevident. For a particular body, low Reynolds number flows are laminar and highReynolds number flows are mostly turbulent.The Reynolds number may be viewed another way:The viscous forces arise because of the internal friction of the fluid. The inertiaforces represent the fluid's natural resistance to acceleration. In a low Reynoldsnumber flow, the inertia forces are negligible compared with the viscous forces,whereas in a high Reynolds number flow, the viscous forces are small relative tothe inertia forces. An example of a low Reynolds number flow (called Stoke'sflow) is a small steel ball dropped into a container of heavy silicon oil. The ballfalls slowly through the liquid; viscous forces are large. Dust particles settlingthrough the air are another case of a low Reynolds number flow. These flows arelaminar. In a high Reynolds number flow, such as typically experienced in theflight of aircraft, both laminar and turbulent flows are present.Surface roughness also affects a body immersed in a flow field. Surfaceroughness causes the flow near the body to go from laminar to turbulent. As thesurface roughness increases, the first occurrence of turbulent flow will moveagainst the direction of the flow along the airfoil. The Reynolds number andsurface roughness are not independent of each other and both contribute to thedetermination of the laminar to turbulent transition. A very low Reynoldsnumber flow will be laminar even on a rough surface and a very high Reynoldsnumber flow will be turbulent even though the surface of a body is highlypolished.Another important factor in the transition from laminar to turbulent flow is thepressure gradient in the flow field. If the static pressure increases withdownstream distance, disturbances in a laminar flow will be amplified andturbulent flow will result. If the static pressure decreases as distance in thedirection of the airflow increases, disturbances in a laminar flow will damp out(or decrease) and the flow will tend to remain laminar. Over an airfoil, thestatic pressure decreases up to the point of maximum thickness. A laminar flow