Theories of dimensional analysis in engineering:

• Casson's model governs plastic fluid flow.
• Davis's theorem relates to electrical circuit theory.
• Buckingham's $\Pi$ (Pi) Theorem is the foundational theorem of dimensional analysis in fluid mechanics and heat transfer, stating that if an equation involving $n$ physical variables has $m$ fundamental dimensions, it can be reformulated into $(n - m)$ independent dimensionless $\Pi$-groups (e.g., Reynolds, Nusselt, Prandtl numbers).
• Maxwell's theorem relates to reciprocal deflections in structural mechanics.

Creep flow dynamics and Stokes' settling/creaming velocity:

• Balancing buoyancy force and hydrodynamic Stokes drag ($F_d = 3\pi \mu D_p v_t$) for a spherical droplet of diameter $D_p$ yields: $v_t = \frac{g D_p^2 (\rho_p - \rho)}{18 \mu}$ (or with fat density lighter than skim serum, creaming upward with velocity proportional to density difference $(\rho - \rho_p)$).
• The denominator $24\mu$ corresponds to drag coefficient formulations ($C_D = 24/Re$), not the integrated terminal velocity expression where the factor is 18.
• Using particle radius $R_p$ with denominator $18\mu$ is incorrect; the radius formulation requires a denominator of $9\mu$ ($v_t = \frac{2 g R_p^2 \Delta\rho}{9 \mu}$).
• Using linear radius $R_p$ violates dimensional homogeneity (velocity must depend quadratically on particle size).

In fluid agitation and mixing tanks, a deep central vortex draws in air and reduces mixing efficiency. Standard engineering methods to prevent vortexing include: (1) installing wall baffles, (2) off-center/eccentric mounting of the agitator, and (3) tilting the impeller shaft angle. A paring disc is a stationary centripetal pump located inside centrifugal separators to discharge clarified liquid under pressure, having no role in preventing vortex formation in mixing tanks.

Option analysis:

• Tilted impeller shaft: Standard geometric technique to suppress tangential swirling and vortexing.
• Agitator mounted on side (eccentrically) of tank: Breaks circular symmetry and prevents centralized vortex formation.
• Use of baffles: Most common and effective method to convert circular flow into axial and radial mixing.
• Using paring disc: Correct, it is a discharge mechanism in milk centrifuges, not an anti-vortex method for tanks.