Agitation power in the turbulent regime: during fully turbulent mixing in a baffled tank, power consumption is primarily proportional to which liquid property?

Introduction / Context:In mixing, the dimensionless power number Np relates impeller power to liquid properties, impeller speed, and diameter via P = Np * ρ * N^3 * D^5 for baffled tanks. Recognizing which properties matter in the turbulent regime guides scale-up and energy estimates.

Given Data / Assumptions:

• Baffled tank, radial/turbine or pitched-blade impeller.
• High Reynolds number based on impeller diameter (fully turbulent).
• Constant Np in the turbulent asymptote.

Concept / Approach:At high Reynolds number, viscous effects are negligible in the global power correlation; Np tends to a constant for a given geometry. The power draw scales linearly with fluid density ρ and with N^3 D^5. Surface tension and thermal conductivity do not feature in the standard mechanical power equation for turbulent agitation.

Step-by-Step Solution:Use P = Np * ρ * N^3 * D^5 (turbulent regime).Holding geometry and speed fixed, P ∝ ρ.Therefore, density is the relevant property.

Verification / Alternative check:Experimental power curves show plateau Np at high Re, confirming independence from viscosity in this regime; density shifts absolute power linearly.

Why Other Options Are Wrong:Viscosity: important at low Re; negligible for fully turbulent power draw.Surface tension/thermal conductivity: not in the mechanical power correlation.

Common Pitfalls:Applying laminar correlations (P ∝ μ) in turbulent scale-up; mixing regimes must be identified correctly before calculations.

Final Answer:density