Number for mixing

The film coefficient h is for the inner wall Dj is the inside diameter of the mixing vessel. The term L N p/ is the Reynolds number for mixing in which L is the diameter and Nr the speed of the agitator. Recommended values of the constants a, b, andm are given in Table 18-2. 

The Reynolds number for mixing ReM represents the ratio of the applied to the opposing viscous drag forces. 

It can be shown by dimensional analysis [Holland and Chapman] that the power number Po can be related to the Reynolds number for mixing ReM, and the Froude number for mixing FrM, by the equation... 

The Weber number for mixing WeM is only of importance when separate physical phases are present in the liquid mixing system as in liquid-liquid extraction. 

A power curve is a plot of the power function 4> or the power number Po against the Reynolds number for mixing ReM on log-log coordinates. Each geometrical configuration has its own power curve and since the plot involves dimensionless groups it is independent of tank size. Thus a power curve used to correlate power data in a 1 m3 tank system is also valid for a 1000 m3 tank system provided that both tank systems have the same geometrical configuration. 

In the fully turbulent flow region DE, the curve becomes horizontal and the power function is independent of the Reynolds number for mixing ReM. For the region ReM > 10000... 

The power curve in Figure 5.8 for the baffled system is identical with the power curve in Figure 5.9 for the unbaffled system up to point C where ReM = 300. As the Reynolds number for mixing ReM increases beyond point C in the unbaffled system, vortexing increases and the power falls sharply. 

A plot of Po against ReM on log-log coordinates for the unbaffled system gives a family of curves at ReM > 300. Each curve has a constant Froude number for mixing FrM. 

A plot of Po against FrM on log-log coordinates is a straight line of slope y at a constant Reynolds number for mixing ReM. A number of lines can be plotted for different values of ReM. A plot ofy against log ReM is also a straight line. If the slope of the line is —1//3 and the intercept at Reu = 1 is a//3 then... 

If a power curve is available for a particular system geometry, it can be used to calculate the power consumed by an agitator at various rotational speeds, liquid viscosities and densities. The procedure is as follows calculate the Reynolds number for mixing ReM , read the power number Po or the power function from the appropriate power curve and calculate the power PA from either equation 5.13 rewritten in the form... 

Read the Reynolds number for mixing ReM from the appropriate Newtonian power curve for each value of Po and N. 

Consider the scale-up of the rotational speed of marine propellers for the same power consumption and Reynolds number for mixing. 

The corresponding equation for equality of Reynolds numbers for mixing has already been shown to be... 

This criterion is recognized as the Reynolds number for mixing in a fluid. 

This criterion is recognized as the Fourier number for mixing time in liquid media. finally, for this case, we can express the result of dimensional analysis as ... 

The similarity of the Euler number (the group is a form of the Euler number for mixing) requires ... 

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