I am confused about Reynolds number. I am trying to use the formula to see if NASCAR cars have laminar or turbulent flow. But I am not sure how exactly to use the equation in order to do such calculation.
[Physics] Misunderstanding about Reynolds number
estimationfluid dynamicsturbulence
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Turbulence isn't the same as unsteadiness - a vortex street is not necessarily a turbulent phenomenon. As an analogy that (for some reason) I find easier to understand, consider a convection experiment where we heat a fluid at the bottom and cool it at the top. Below a certain threshold value for the temperature difference, the heat is transferred only by diffusion and there is no bulk flow. A little higher and we get an instability, resulting in the formation of a convection cell. In this case the fluid is moving, but it is still moving in a laminar way. As we increase the temperature difference, the speed of the flow increases, and it's only when we've increased the temperature quite a bit more that the flow becomes turbulent.
Vortex streets are similar. Above a certain value of the Reynolds number, the vortex street forms. The flow is now time-dependent, but it's periodic and still relatively easy to predict. If the flow is increased even further then the vortices spin so fast that smaller vortices form to dissipate their kinetic energy. It's only at this point that the flow becomes unpredictable and chaotic, which is when we call it turbulent. I guess you can say something like, a Kármán vortex street is a flow that's unsteady on one spatial scale, but in order for a flow to be called turbulent it has to be unsteady across a wide range of scales.
The flow behind the screen with the grid has a specific structure unlike the flow in the pipe - see fig.1. First, the flow is uniform across the channel, which is important for aerodynamic experiments. Secondly, the transition to turbulence occurs in the boundary layer at large Reynolds numbers, and the core of the flow remains unperturbed. All this allows to realize the laminar flow in the wind tunnel even at a flow velocity of 10-25 m / s. Figure 1 shows the magnitude of velocity (left), the velocity profile at the outlet (in the center) and the longitudinal component of velocity in a laminar flow in a channel behind the grid.
Best Answer
Use the Reynolds number equation:
$Re={vL \over \nu}$
where $\nu\approx 1.5\times10^{-5}m^2/s$ is the kinematic viscosity for air. If you enter this into the equation, you end up with
$Re\approx 67000{v\over{m/s}}{L\over m}$
i.e. for a race car traveling at 40m/s and with a length of 4m it comes out to be around 10 million, which is certainly $Re>>1$, i.e. in a regime far beyond the requirement for the Stokes formula to be a good approximation.