Reynolds number similarity

The experimental results of Mayer indicate that the wave velocity is proportional to NK (M7). Since u is proportional to [Eq. (18)], it follows that the ratio c/u must decrease with increasing Reynolds numbers. Similar experimental conclusions have been reported elsewhere also, e.g. (F7). 

A duct 4 ft in diameter with a 90 bend has been designed to carry particles In the range I < dp < 20 which adhere when they strike the wall. Before construction, it is proposed to carry out bench scale experiments to determine the particle deposition rate in the bend. The model is to be built to 1/10 scale, and the same aerosol will be used as in the full-scale system, Show that it is not pos.siblc to ntainlain both Stokes and Reynolds number similarity in the full-scale and model systems. If Stokes similarity is to be preserved, calculate the Reynolds number ratio for the model to full-scale systems. Why is it more important to preserve Stokes than Reynolds similarity in such experiments ... 

The term (cfl2), represents the skin friction coefficient corresponding to a constant-property boundary layer at the same local length Reynolds number. Similarly, the Stanton number is given by... 

The exact shape of the velocity profile in the outflow of an impeller does not depend solely on the impeller. It is also affected by such variables as the impeller Reynolds number, impeller off-bottom distance C/T, and impeller diameter D/T. If the flow is fully turbulent (i.e.. Re > Kf ), the impeller outflow profiles are typically independent of Reynolds number. If the flow is flansitional or laminar, however, care should be taken so that the velocity profiles used were either measured at a similar Reynolds number, or that the prescribed velocities are being interpolated from data sets measured over a range of Reynolds numbers. Similarly, for impeller off-bottom clearance and diameter, if data for various C/T and D/T values are available, interpolations can be used to obtain the prescribed velocities for the actual conditions. 

Constant Reynolds number Similar heat transfer from jacket walls equal viscous/inertial forces. 

The Nusselt number is independent of the Reynolds number, similar to that of macrochannel flow. 

An additional problem in achieving Reynolds-number similarity is that, when comparing the performance of one industrial cyclone with that of another, obtaining data at the same Re for the two is often not possible. 

But is it really necessary to scale-up cyclones on the basis of Re similarity A redeeming feature is that, in many cases, Reynolds number similarity is not very critical. This has long been known, but the issue has only been studied quantitatively recently, by Overcamp and Scarlett (1993), among others. They deflned Re and Stk in terms of the inlet velocity. We shall use the symbols Rein and Stkm, respectively. Figure 8.2.1 shows a plot of the square root of Stkin50 against Re for a wide range of cyclones, taken from their paper. 

This is the formal requirement for dynamic similarity, and is consistent with the results of the classical dimensional analysis in the main text. As we mentioned there, experience teaches us that over a wide range of operating conditions Reynolds number similarity is not all that critical for Stokes number similarity between cyclones, and this indicates that, in this range, it is not all that critical for dynamic similarity. 

Determine the velocity at which we would have to operate a 6 (152 mm) diameter model cyclone to obtain Reynolds number similarity to a 48 (1220 mm) industrial cyclone. 

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