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The dimensionless Reynolds number is an important parameter in the equations that describe whether fully developed flow conditions lead to laminar or turbulent flow. The Reynolds number is the ratio of the inertial force to the shearing force of the fluid: how fast the fluid is moving relative to how viscous it is, irrespective of the scale of ...
With respect to laminar and turbulent flow regimes: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion; turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.
In case of laminar flow, the velocity profile in the fully developed region is parabolic but in the case of turbulent flow it gets a little flatter due to vigorous mixing in radial direction and eddy motion. The velocity profile remains unchanged in the fully developed region. Hydrodynamic Fully Developed velocity profile Laminar Flow :
where Re is the Reynolds number, ρ is the fluid density, and v is the mean flow velocity, which is half the maximal flow velocity in the case of laminar flow. It proves more useful to define the Reynolds number in terms of the mean flow velocity because this quantity remains well defined even in the case of turbulent flow, whereas the maximal ...
The new "inner length scale" is a viscous length scale, and is of order , with being the velocity scale of the turbulent fluctuations, in this case a friction velocity. Unlike the laminar boundary layer equations, the presence of two regimes governed by different sets of flow scales (i.e. the inner and outer scaling) has made finding a ...
In fluid mechanics, plug flow is a simple model of the velocity profile of a fluid flowing in a pipe. In plug flow, the velocity of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe. The plug flow model assumes there is no boundary layer adjacent to the inner wall of the pipe.
Also of interest is the velocity profile shape which is useful in differentiating laminar from turbulent boundary layer flows. The profile shape refers to the y-behavior of the velocity profile as it transitions to u e (x). Figure 1: Schematic drawing depicting fluid flow entering the bottom half of a 2-D channel with plate-to-plate spacing of H.
Compared to turbulent flow, laminar flow tends to have a lower velocity and is generally at a lower Reynolds number. Turbulent flow, on the other hand, is irregular and travels at a higher speed. Therefore the flow velocity of a turbulent flow on one cross section is often assumed to be constant, or "flat". The "non-flat" flow velocity of ...