P N D

Thus,

where /VRc is the Reynolds number and

PL is the liquid viscosity. Yet another dimensionless number, termed the Froude number, relates inertial force to gravitational force and is given the term:

where NFr is the Froude number and g is the gravitational force. Rushton et al. (1950) demonstrated that the power number was related to the Reynolds and Froude numbers by the general expression:

where c is a constant dependent on vessel geometry but independent of vessel size, x and y are exponents. Examples of the values of c, x and y are considered later.

However, in a fully baffled agitated vessel the effect of gravity is minimal so that the relationship between the power number and the other dimensionless num

Therefore substituting from equations (9.16) and (9 17).

P/( pN3D5) = c( pDzN/p,y (9 21) Values for P at various values of N, D, /x and p m-, be determined experimentally and the Reynolds and power numbers for each experimental situation mav then be calculated. A plot of the logarithm of the power number against the logarithm of the Reynolds number yields a graph termed the power curve. A typical power curve for a baffled vessel agitated by a flat-blade turbine is illustrated in Fig. 9.15 and such a curve would apply to geometrically similar vessels regardless of size.

From Fig. 9.15 it may be seen that a power curve is divisible into three clearly defined zones depicting different types of fluid flow:

(i) The laminar or viscous flow zone where the logarithm of the power number decreases linearly with an increase in the logarithm of the Reynolds number. The slope of the graph is equal to x, the exponent in equation (9.21) and is obviously equal to -1. The power absorbed in this region is a function of the viscosity of the liquid and the Reynolds number is less than 10.

(ii) The transient or transition zone, where there is no consistent relationship between the power and Reynolds numbers. The value of x (that is, the slope of the plot) is variable and the value of the Reynolds number is between 10 and 104.

(iii) The turbulent flow zone, where the power number is a constant, independent of the

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