Everything, Everywhere
Verified Specification | Standardized Formulas | Instant Precision
Secure & Private (Zero Data Retention) Free Access • No Sign-Up
FLUID MIXING & AGITATION ENGINEERING

Agitator Impeller Power, Reynolds & Blend Time Calculator

Size industrial mixing impellers (Rushton, Pitched Blade, Hydrofoil, Marine, Anchor). Compute mixing Reynolds number, power draw (Np), 95% blend time, tip shear speed, and bulk pumping turnover.

Vessel & Impeller Geometry

meters inside diameter
meters liquid batch height
meters (typically D/T = 0.25 to 0.50)
RPM (rev per minute)
dimensionless power number

Fluid Properties & Tank Baffling

kg/m³
cP (mPa·s, water = 1 cP)
% mechanical transmission

Agitation Power & Hydrodynamic Metrics

Shaft Impeller Power
--
--
Mixing Reynolds (Re_m)
--
--
95% Blend Time (t_95)
--
--
Impeller Tip Speed
--
--
Specific Power Density
--
--
Pumping Flow Rate (Q_p)
--
--
Batch Volume
--
D / T Ratio
--
Froude Number
--

Mixing Tank Circulation Patterns & Surface Vortex Profile

5 Fatal Industrial Traps in Agitator & Impeller Design

1. The Deep Central Vortex Air Entrainment & Shaft Whiplash Trap

In unbaffled tanks with high-speed impellers, centrifugal body forces swirl the entire liquid mass as a solid-body vortex. The surface vortex reaches down into the impeller blades, entraining massive volumes of air. The asymmetric gas pockets create violent periodic hydraulic imbalances that whip the overhung shaft sideways, snapping mechanical seal faces and wrecking gearbox bearings.

2. Viscosity-Thinning Power Surge in Transitional Regimes

In non-Newtonian or temperature-thinning polymer batches, mixing starts in the laminar regime ($Re < 10$) where power scales with speed squared ($P propto N^2$). As temperature rises and viscosity drops by 90%, the fluid transitions into turbulent flow ($Re > 10^4$) where power scales with speed cubed ($P propto N^3$). Motors sized without thermal transition margin overload and trip on thermal breaker.

3. Shear Damage in Mammalian Bioreactors & Emulsion Inversion

Selecting a high-shear radial turbine (such as a Rushton turbine, tip speed $> 4.0 ext{ m/s}$) for mammalian cell cultures (CHO cells) tears cell membranes and drops cell viability to zero within 24 hours. Delicate biological and crystallization processes require low-shear, high-solidity axial hydrofoils (A310 or HE-3) operating at tip speeds under $1.8 ext{ m/s}$ to provide bulk fluid motion without destructive shear gradients.

4. Solid Settling Fillet Formation from Sub-Zwietering Speed ($N < N_{js}$)

When suspending catalyst beads, slurry crystals, or polymer beads, running below the Zwietering just-suspended speed ($N_{js}$) leaves solids stagnant in corners and dish fillets. These dead zones form compacted cakes that resist resuspension, causing localized hot spots, thermal runaway, or unreacted raw material dump during tank discharge.

5. Shaft Critical Speed Resonance ($N_{crit}$) Catastrophe

Long overhung agitator shafts exhibit mechanical natural frequencies. Operating within 20% of the first lateral critical speed ($0.8 N_{crit} < N < 1.2 N_{crit}$) excites harmonic resonance. The shaft deflects wildly until it either impacts tank wall baffles, shears off at the rigid coupling, or punctures the vessel shell.

Governing Equations: Impeller Power Number & Mixing Hydrodynamics

1. Mixing Reynolds Number ($Re_m$):

Re_m = rac{ ho cdot N_{rev/s} cdot D^2}{mu} = rac{ ho cdot (RPM / 60) cdot D^2}{mu_{Pacdot s}}

2. Shaft Power Consumption ($P$): In fully baffled turbulent flow ($Re_m > 10^4$):

P = N_p cdot ho cdot N_{rev/s}^3 cdot D^5 quad [ ext{Watts}], quad P_{motor} = rac{P}{eta_{trans}}

For laminar flow ($Re_m < 10$): $N_p propto 1 / Re_m implies P = K_L cdot mu cdot N^2 cdot D^3$.

3. 95% Blend Time ($t_{95}$, Grenville & Tilton Correlation):

N_{rev/s} cdot t_{95} = rac{5.4}{N_p^{1/3}} cdot left( rac{T}{D} ight)^2 implies t_{95} = rac{5.4 cdot T^2}{N_{rev/s} cdot N_p^{1/3} cdot D^2} quad [ ext{seconds}]

4. Pumping Flow Rate ($Q_p$) & Bulk Turnover:

Q_p = N_q cdot N_{rev/s} cdot D^3 quad [ ext{m}^3/ ext{s}], quad t_{turnover} = rac{V_{batch}}{Q_p}

Frequently Asked Questions

What is the Impeller Power Number (N_p) and how does it determine motor sizing? +
Why are tank baffles mandatory in low-viscosity turbulent mixing? +
How does the Mixing Reynolds Number (Re_m) distinguish flow regimes? +
What is the 95% blend time (t_95) and how is it calculated? +
What causes shaft critical speed resonance in industrial mixers? +
Sponsored Utility
While You're Here
Sponsored Recommendations
Advertisement