Terminal speed drops

Wallis, G.B., The terminal speed of liquid drops and bubbles in an infinite medium, International Journal ofMultiphase Flow, l,pp. 491-511 (1974). 

Wallis GB (1974) The terminal speed of single drops or bubbles in an infinite medium. Int J Multiphase Flow 1 491-511... 

For a liquid drop held spherical by surface tension, the terminal speed from Eq. (5.1.4) is given by... 

During a run, if the supply voltage to a motor terminal drops to 85% of its rated value, then the full load torque of the motor will decrease to 72.25%. Since the load and its torque requirement will remain the same, the motor will star to drop speed until the torque available on its speed-torque curve has a value as high as 100/0.7225 or 138.4% of T to sustain this situation. The motor will now operate at a higher slip, increasing the rotor slip losses also in the same proportion. See equation (1.9) and Figure 1.7. 

Not until the above effects can be mathematically related can we expect to progress beyond the experimental stage. To predict such items as size of drop formed at a nozzle, terminal velocity, drag curves, changes of oscillations, and speed of internal circulation, one must possess experimental data on the specific agent in the specific system under consideration. Davies (Dl, D2) proposes the use of the equation... 

One can also find a functional form for the trajectory of the large droplets that are formed at the CBL. The path of these droplets represents the maximum spray penetration. Since they are not connected to the jet and are in direct contact with a strong gas flow, they do not necessarily follow a path of the form of (29.9) anymore. A schematic view of the trajectory of these drops is shown in Fig. 29. Ic with a local coordinate system attached to the CBL for convenience. In general most applications of LJICF are concerned with high momentum ratios for which the jet deflection is not pronounced. For those cases, it is fair to assume that the droplets formed at the CBL have a zero initial velocity in the x-direction as they separate fi om the jet and have an initial upward velocity of mj. As these droplets leave the jet, they lose their vertical velocity and speed up in the gas-streamwise direction and finally reach their terminal x-direction velocity. Of course, all these are true for one droplet without considering its interaction with other droplets and also with neglecting the effects of evaporation. With these assumptions, the equations governing the motion of the drop take the form... 

The motor is sized for continuous operation at the flows resulting from four-pump or one-pump operation with 1.0 to 0.74 specific gravity water. The motors are designed to start and accelerate to speed under full load with a drop to 80 percent of normal rated voltage at the motor terminals. 

All of the droplets then hit the ground. In cascades with high liquid mass flux densities the droplet impact speed may considaably exceed the terminal velocity for a single drop. Again the number and size of smaller secondary droplets formed on impact depends on the surface tension, impact speed and the nature of the impact surface ie wetted solid or deep liquid. 

A nickel ore slurry needs to flow by gravity at a weight concentration of 28%. The design flow rate is 1631 m /hr. The slurry was tested in a 159 mm pipeline with a roughness coefficient of 0.016 mm at a weight concentration of 26.3%. The results of the pressure drop versus speed are presented in Table 4-2. No data was made available on the drag coefficients or terminal velocity of the solids. 

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