Understanding the Reynolds Number for Mixing Tank

The Reynolds number helps determine how the fluid moves inside the tank (or in a pipe).

To make it simple, the Reynolds number tells you whether the liquid wants to flow easily or resist movement and when transition will take place.

Designing an agitator without considering the Reynolds number often leads to:

• Over-sized mixer and unnecessary energy consumption
• Under-performing mixer with dead zones and poor process results
• Increased equipment wear, maintenance, and operating costs

Optimizing impeller design and operating parameters for the right flow regime delivers superior performance and long-term efficiency.

When selecting or designing a tank mixer, the Reynold number helps predict how the fluid will respond to agitation and whether the mixer can achieve the desired blending, dilution, suspension, or homogenization.

It defines the flow regime, from laminar to turbulent flow. Knowing the flow regime is crucial for choosing the right impeller type and mixer rotation speed, ensuring optimal energy transfer without waste.

In industrial mixing, turbulent flow is typically the desired regime, because it reduces stagnant zones and improves mass transfer.

Because the Reynolds number is dimensionless, it is independent of the unit system or the relative size of the system. The only requirement is to keep units consistent, such as using SI units as in our example.

When mixing in a tank, the Reynolds number (Re) tells us how the fluid will flow. The appearance of turbulent motion corresponds to a Reynolds number of about 3,000.

As this number rises, turbulence increases, leading to noticeable changes in the mixing operation appearance. This becomes completely turbulent for a Reynolds number above 6,000.

• Re < 3,000: the flow is laminar.

The flow is slow and smooth and layered, meaning that two separate flows move in the same direction in parallel layers, involving a slow mixing.

This occurs with high viscous fluids like adhesives, polymers, wastewater sludge or creams. Low-shear impellers are used to avoid damaging the product. 

• 3,000 < Re < 6,000: the flow is transitional, unstable, in between the two states.

This occurs with fluids having medium‑viscosity such as syrups and slurries.

• Re > 6,000 the flow is turbulent. In industrial mixing, turbulent flow is generally the ideal condition to achieve.

In turbulent regime, the fluid doesn’t flow in layers. The flow is chaotic, energetic, involving an energic mixing, much faster to allow good dispersion and maintain in suspension.

This is the most common flow regime in the industry where industrial mixers are used. Water and solvents for instance, both are low viscous products that can be easily mixed.

Calculation example with water:

Water at 20 °C (68 °F): ρ ≈ 1000 kg·m⁻³, μ ≈ 0.001 Pa·s

• Impeller diameter: D = 2 m
• Mixer Rotation Speed: 180 rpm. Then N = 180/60 = 3 s⁻¹

With Re = 12,000,000: the flow is turbulent. Expect strong blending, good suspension (with proper off‑bottom clearance and baffles).

The Reynolds number directly influences several parameters when selecting and designing a mixer:

Impeller type

• Low Re / Laminar flow: Radial‑flow impellers are used such as anchor, helical ribbon, double-helical. Large impeller diameters are preferred.
• Transitional flow: Pitched blade turbines or axial‑flow impellers, often multiple stages.
• High Re / Turbulent flow: Axial‑flow impellers such as hydrofoils or radial‑flow impellers such as Rushton turbines.

Impeller diameter (D)

A larger impeller increases the Reynolds number (as D²), leading to more effective mixing.

• Larger impeller diameter boosts Re strongly.
• Anchors with typically D/T ratio ranging from 0.7 to 0.95.
• Axial‑flow impellers like HXP generally have a D/T ratio ranging from 0.3 to 0.5.

Mixer Rotation Speed (N) and Motor Power

Speeding up the mixer rotational speed (N) increases Reynolds number and push the flow toward turbulence:

• Increase N to push into turbulence when feasible.
• Low Re favors high torque and low speed, involving increasing the motor power. Adjust based on power and torque limits.

Fluid viscosity (μ)

High viscous fluids, meaning a low Re, are harder to mix, and risk stagnant zones.