Application of Scale-Up in Stirred Vessels

During the mixing of a single-phase liquid in a stirred tank, the important parameters are the rate of power input, P, the impeller stirring speed, N, gravitational acceleration, g, the fluid density, p and viscosity, p, the impeller diameter, D and the other geometric characteristic lengths of the vessel (i.e. baffle width and depth, impeller shape, 

Assuming geometric similarity, dimensional analysis yields the following dimensionless groups  

The Froude number is associated with the formation of a vortex on the liquid free surface around the impeller shaft. At low impeller speeds 

See Chapter 3, Concepts of Fluid Flow for experimental details of Po versus Re relationships. 

1 Scale-Up at Constant Re/. For a given fluid, Re oc NO2 = constant, i.e. N cc D 2. Scale-up at constant Rei implies constant Po, yielding, for a given fluid, P oc N2 If. Therefore, scale-up at constant Re gives P oc N2D5 cc (D 2)2 x D5 oc D l. Power requirement decreases as scale increases This is not a suitable scale-up criterion. 

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