Mixing and scale-up terminology: In agitator design, the power number (Np) used in impeller power correlations is also known by which classical non-dimensional name?

Introduction / Context:The power number, Np, is a dimensionless group widely used to correlate impeller power draw in stirred tanks: Np = P / (ρ * N^3 * D^5), where P is power, ρ is liquid density, N is rotational speed, and D is impeller diameter. Many dimensionless groups have historical names; recognizing equivalences is important for reading classic literature and vendor data sheets.

Given Data / Assumptions:

• We refer to standard fluid-mechanics nomenclature.
• Np relates power to inertial scaling N^3 D^5.
• No special flow regime restrictions are added in the stem.

Concept / Approach:In classical fluid dynamics, Np is called the Newton number. It quantifies the ratio of viscous dissipation power to inertial reference power for a rotating mixer, and is often presented as a function of Reynolds number Re = ρ N D^2 / μ and sometimes Froude number in gas–liquid systems.

Step-by-Step Solution:

Verification / Alternative check:Standard mixing texts and impeller vendor catalogs show Np labeled as Newton number; plotted as Np versus Re for different impeller types (Rushton, pitched blade, hydrofoil).

Why Other Options Are Wrong:

• Froude number relates inertia to gravity (important for vortex formation and gas dispersion).
• Bond number compares gravity to surface tension effects.
• Rayleigh number is a buoyancy-driven convection parameter (thermal or compositional).
• Euler number concerns pressure drop relationships, not power draw scaling here.

Common Pitfalls:Confusing Np with Fr in aerated systems; both can enter correlations, but they are distinct groups with different physical meanings.

Final Answer:Newton\'s number