Q: Impeller Reynolds number (Rei): What numerical range corresponds to laminar mixing in agitated tanks based on the impeller Reynolds number definition?

Introduction / Context:The impeller Reynolds number Rei = ρ * N * D^2 / μ is used to classify flow regimes in mixing: laminar, transitional, or turbulent. Correctly identifying the laminar range helps choose impeller types and predict power and blending times, especially for viscous or polymer-containing fluids. Given Data / Assumptions: Standard definition of Rei with density ρ, speed N, impeller diameter D, and viscosity μ. Newtonian fluid assumption for regime boundaries. Baffled tank unless otherwise specified. Concept / Approach:Typical regime cutoffs in mixing practice are: laminar for Rei less than about 10, transitional for roughly 10 to 10^4, and fully turbulent above about 10^4. In the laminar regime, power number varies inversely with Rei and flow is dominated by viscous effects, making axial/radial distinctions less meaningful than in turbulent flow. Step-by-Step Solution: Recall Rei expression and regime thresholds used in design charts.Match “laminar” with Rei below approximately 10.Confirm transitional and turbulent ranges exceed this value.Select Rei 10^4: turbulent. “None”: recognized boundaries exist. 100–1000: sits well inside transitional for mixing practice. Common Pitfalls:Using pipe-flow Reynolds thresholds; mixing thresholds differ because geometry and rotating flow modify transitions. Final Answer:Rei < 10

Question 1

Gas–liquid mixing power: Compared at the same rotational speed, how does the power drawn by an agitator change when the system is gas-sparged versus gas-free?

Accepted Answer

Introduction / Context:When gas is sparged into a mechanically agitated vessel, bubbles alter local density, slip velocities, and blade loading. Engineers must know whether gassing increases or decreases the impeller power draw at fixed speed, because this influences motor sizing and scale-up correlations. Given Data / Assumptions: Agitator speed is the same in both cases. Geometry and liquid properties are unchanged. Gas holdup is in the typical industrial range (no flooding or complete gas disengagement anomalies). Concept / Approach:In most practical regimes, introducing gas lowers the measured power draw at constant speed compared to ungassed operation. The gas phase displaces liquid near the blades, reduces effective density, and modifies circulation patterns, resulting in a “gas-induced power reduction.” This is captured in correlations using a power reduction factor Pg/Pu < 1, where Pu is ungassed power and Pg is gassed power at identical N. Step-by-Step Solution: Hold N constant and introduce gas to the vessel.Observe that torque on the shaft typically decreases with bubble presence.Hence measured power P = 2π N * torque drops versus the ungassed case.Conclude: power is lesser in a gas-sparged system at the same speed. Verification / Alternative check:Power curves from literature plot Pg/Pu as a function of superficial gas velocity and impeller type; values generally fall below 1 until flooding transitions complicate behavior. Why Other Options Are Wrong: More than/same as: contradict the typical reduction effect. “None”: a clear trend exists. “Greater only at very low Re”: not a general rule. Common Pitfalls:Confusing power draw with oxygen transfer; KLa can increase with gas even as power falls. Final Answer:Lesser than in a gas-free system

Question 2

Impeller Reynolds number (Rei): What numerical range corresponds to laminar mixing in agitated tanks based on the impeller Reynolds number definition?

Accepted Answer

Introduction / Context:The impeller Reynolds number Rei = ρ * N * D^2 / μ is used to classify flow regimes in mixing: laminar, transitional, or turbulent. Correctly identifying the laminar range helps choose impeller types and predict power and blending times, especially for viscous or polymer-containing fluids. Given Data / Assumptions: Standard definition of Rei with density ρ, speed N, impeller diameter D, and viscosity μ. Newtonian fluid assumption for regime boundaries. Baffled tank unless otherwise specified. Concept / Approach:Typical regime cutoffs in mixing practice are: laminar for Rei less than about 10, transitional for roughly 10 to 10^4, and fully turbulent above about 10^4. In the laminar regime, power number varies inversely with Rei and flow is dominated by viscous effects, making axial/radial distinctions less meaningful than in turbulent flow. Step-by-Step Solution: Recall Rei expression and regime thresholds used in design charts.Match “laminar” with Rei below approximately 10.Confirm transitional and turbulent ranges exceed this value.Select Rei < 10 as the laminar regime. Verification / Alternative check:Power-number correlations (Np vs Rei) show linear laminar scaling for Rei < 10; deviations begin as inertia grows in the transitional regime. Why Other Options Are Wrong: 10–10^4: transitional. >10^4: turbulent. “None”: recognized boundaries exist. 100–1000: sits well inside transitional for mixing practice. Common Pitfalls:Using pipe-flow Reynolds thresholds; mixing thresholds differ because geometry and rotating flow modify transitions. Final Answer:Rei < 10

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