Step 1: Understanding the Concept:
Unit operations in process engineering: Agitation refers to forcing a fluid/material by mechanical means into circulatory or pattern motion inside a vessel, whereas Mixing is the random distribution of two or more separate phases into a homogeneous whole.
Key Formula or Approach:
\[ \text{Mechanical Power Input } (P = N_p \rho N^3 D^5) \xrightarrow{\text{Impeller Circulation}} \mathbf{Mixing \text{ and } Agitation} \]
Step 2: Detailed Explanation:
In chemical and dairy engineering unit operations:
1. Agitation: Defined formally as the application of mechanical force (via rotating impellers, paddles, propellers, or turbines) to move a material in a circulatory or specific flow pattern inside a vessel (B).
2. Mixing: The blending of two or more initially separate phases (liquids, solids, or gases) into an intimate, uniform, homogeneous state.
- In standard dairy technology textbooks and process terminology (McCabe, Smith, and Harriott Dairy Plant Engineering), this combined mechanical operation is formally designated as Mixing and agitation.
Step 3: Final Answer:
Therefore, the process application of mechanical force is Mixing and agitation, corresponding to option (B).