Bagnold number

Velocity distribution measurements in the polystyrene slurries showed that k in the slurry is somewhat higher than the clear fluid value of 0.4. Using estimated y values, the Bagnold numbers were <450 in all cases and <40 for the fine particles. It appears Bagnold s criterion does not apply to these turbulent flows. 

Bagnold number, Ba d YP fJ- p particle density y velocity gradient d particle diameter p, fluid Gscosity particle collissional force fluid viscous force Granular flows... 

Since B varies inversely with particle diameter, we see that with small particles the effect of the wind is greater than that of gravity. Hence we conclude that such particles conform nearly to the motion of the fluid., stream in which they are carried. Let us examine Eq (19-13) more closely. The constant CR is obviously a function of Reynolds number which for streamline motion is equal to 24/R and for turbulent motion has a constant value of 0.4. Hence for Bagnold s number we may write ... 

Bagnold has determined the Reynolds number which fixes either the critical diameter or the threshold velocity gradient. He has found that when... 

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