ANS:D - all geometrical, dynamic and kinematic similarity.

Scale-up of agitator design requires both geometrical and dynamic similarity.

Explanation:

1. Geometrical Similarity:
   • Geometrical similarity ensures that the scaled-up agitator has the same proportions and dimensions as the original agitator. This includes maintaining the same blade geometry, diameter, shaft length, and clearance from the vessel walls.
   • Geometrical similarity helps in ensuring that the flow patterns, mixing efficiency, and power requirements are comparable between the original and scaled-up designs.
2. Dynamic Similarity:
   • Dynamic similarity ensures that the forces acting on the fluid and the agitator (such as shear forces, turbulence intensity, and power consumption) are equivalent in both the original and scaled-up systems.
   • This involves matching the Reynolds number, Froude number, and other dimensionless parameters that govern fluid flow dynamics and mixing characteristics.
3. Kinematic Similarity:
   • Kinematic similarity refers to the similarity in motion between corresponding points in the scaled-up and original agitator systems. It ensures that the velocities and accelerations of fluid elements around the agitator are proportional in both systems.
4. Scale-up Considerations:
   • When scaling up an agitator design, it is crucial to maintain both geometrical and dynamic similarity to ensure that the performance and efficiency of mixing are maintained or improved in the larger system.
   • Simply maintaining geometrical similarity (same dimensions) without considering dynamic similarity (same fluid flow characteristics) may result in inefficient mixing or unexpected flow patterns.

Conclusion: