Incompatibility of Some Equations

It is decided to model a full-scale prototype, unbaffled, stirred vessel with a one-tenth scale model. The liquid in the prototype has a kinematic viscosity, v. of 10 7 m2 s As we have seen above, power number is a function of both Reynolds number and Froude number for unbaffled vessels. To ensure power number similarity, we need to ensure both Reynolds number and Froude number are similar from prototype to model. 

Froude number similarity, as g is constant, NmDm = NPDP, Thus, 

Constant Reynolds number ND2 zr1 Unrealistic scale-up criterion, larger scales require less power  

Constant power per unit volume implies similar turbulence micro-scales N3D2 n3d5 May be difficult to achieve due to large power requirements 

Constant impeller tip speed (often used to limit shear damage to sensitive fluids) ND D2 Industrial rule-of-thumb keep tip speed below 10 m s 1 for shear sensitive products 

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