比栓半径の新しい求め方

スライム輸送に関する研究 (1)

抄録

In such a case that Bingham's fluid flows in laminer flow for circular tube, the equation of pressure drop (P/L) is obtained as follows:
P/L=32μ_BV_D/Dφ=4τ_y/Da where Φ=1-4a/3+a⁴/3
Planning the hydraulic transportation of slurry, the equation must be applied in case that slurry is Bingham's fluid, and the value of plug radius (a) must be determined for calculating pressure drop.
Although the trial method was proposed by E. L. McMillen for determination of plug radius, the method requires much trouble.
Then, a handy method named differential method was induced by the authors. In this method, the value of plug radius is determined by the differential coefffcient (tanθ) of curve which is obtained from the relation between the pressure drop (P/L) and the mean velocity (Vm) of Bingham's fluid plotted on the logarithmic graph.
The relation between of plug radius and the differential coefficient is obtained as follows:
tanθ=1/(1+4a (1-a³)/(3-4a+a⁴))
As the value of plug radius is calculated by the above equation or the (a-θ) diagram, the new method is very convenient in comparison with the trial method. The above relation was certified by the experiment using the slime slime slurry of Ashio mine.