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In that case, the velocity of flow varies from zero at the walls to a maximum along the cross-sectional centre of the vessel. The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements and applying the viscous force to them. [5] Another example is the flow of air over an aircraft wing.
In the case of laminar flow, for a circular cross section: =, =, 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 ...
If the formula for laminar flow is f = 16 / Re , it is the Fanning factor f, and if the formula for laminar flow is f D = 64 / Re , it is the Darcy–Weisbach factor f D. Which friction factor is plotted in a Moody diagram may be determined by inspection if the publisher did not include the formula described above: Observe the ...
Hence, any convective flow, whether turbulent or not, will involve nonlinearity. An example of convective but laminar (nonturbulent) flow would be the passage of a viscous fluid (for example, oil) through a small converging nozzle. Such flows, whether exactly solvable or not, can often be thoroughly studied and understood. [25]
The transition from laminar to turbulent flow. Turbulence is flow characterized by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar. The presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well.
Boundary layer flow over a wing surface begins as a smooth laminar flow. As the flow continues back from the leading edge, the laminar boundary layer increases in thickness. Turbulent boundary layer flow. At some distance back from the leading edge, the smooth laminar flow breaks down and transitions to a turbulent flow.
is the flow velocity relative to the object (meters per second). Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' law makes the following assumptions for the behavior of a particle in a fluid: Laminar flow
An example where the mere Reynolds number is not sufficient for the similarity of flows (or even the flow regime – laminar or turbulent) are bounded flows, i.e. flows that are restricted by walls or other boundaries.