Reference ID: MET-3D0E | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
An anchor impeller operating inside a jacketed cooking kettle mixes highly viscous food products such as starch slurries, sauces, or confectionery masses. Because the viscosity is often 10³–10⁴ cP and speeds are low (< 1 s⁻¹), the flow is laminar and the power draw is governed by viscous forces rather than inertial ones. Accurate prediction of the shaft power is essential for:
Sizing the motor and gearbox so the drive train is neither under- nor over-designed.
Estimating heat-generating mechanical energy that must be removed by the jacket.
Checking torque limitations on the shaft and welded impeller arms.
This sheet delivers the laminar-only correlation validated for close-clearance anchors for Re ≤ 30.
Methodology & Formulas
Step 1 – Convert practical units to SI absolute
\[
N = \frac{N_{\text{rpm}}}{60}\quad[\text{s}^{-1}],\quad
\mu = \frac{\mu_{\text{cP}}}{1000}\quad[\text{Pa·s}]
\]
\[
Po = \frac{P}{\rho\,N^{3}D^{5}},\quad
P = K_{p}\,\mu\,N^{2}D^{3}
\]
where the empirical anchor constant is
\[
K_{p} = 200\ (\pm 25\ \%).
\]
Step 5 – Motor sizing
\[
P_{\text{motor}} = P \times 1.25
\]
Select the next commercially available motor rating above this value.
Start with the laminar correlation for close-clearance anchors: \( Po = K_p Re^{-1} \) where \( K_p \approx 200 \) for standard geometry. This is valid for Re ≤ 30. Always validate these numbers with a viscosity sweep on site.
Estimate an average shear rate from \( \gamma_{\text{avg}} = k \cdot N \) where \( k \approx 12 \) for anchors in laminar flow.
Measure apparent viscosity \( \eta_a \) at this shear rate using your rheogram.
Compute a “viscosity-matched” Reynolds \( Re' = \frac{\rho N D^2}{\eta_a} \) and recalculate power using the standard \( Po–Re \) relation (\( Po = K_p Re^{-1} \)).
Scale-up with constant torque per unit volume: \( P/V \) remains the same if \( Re' \) stays in the same regime.
Monitor motor amperage after scale-up; yield-stress fluids can cause stalled regions that raise torque spikes beyond the isothermal calculation.
Minor sparging (< 0.02 vvm) can drop anchor torque 10–15 % because gas pockets lubricate the blade-wall interface. However, CFD often misses this because most models assume uniform wetting of the wall and ignore the thin viscous sub-layer where the anchor “sees” the drag. If the simulation wall shear is under-predicted by ~20 %, power will be low by roughly the same ratio. Calibrate an “effective roughness” factor of 2–3 wall units into the k-ε model to match plant readings within ±5 %.
Calculate the process-side film coefficient from \( Nu = 0.5 Re^{1/3} Pr^{1/3} (\mu/\mu_w)^{0.14} \) using the anchor Re for laminar flow.
For viscous products the wall-side is often limiting; aim for an overall U that keeps ΔTjacket above 15 °C to avoid crystallization.
Raise agitator speed until power approaches the shaft limit; beyond that switch to a dual-impeller (anchor + pitched blade) to decouple mixing and power draw.
Finally, check that torque fluctuations stay within 15 % of mean—large fluctuations indicate viscoelastic resonance and possible wall overheating.
Worked Example: Anchor Impeller Power Calculation for a Jacketed Cooking Kettle
A process engineer is sizing the drive motor for an anchor impeller in a jacketed kettle used to cook a starch slurry. The impeller must operate at a constant speed to ensure uniform heating and mixing consistency.
Known Input Parameters
Impeller diameter, D = 0.60 m
Rotational speed, N = 30.0 rpm
Dynamic viscosity of the slurry, μ = 8000.0 cP
Fluid density, ρ = 1050.0 kg/m³
Step-by-Step Calculation
Convert the input parameters to SI absolute units as per the internal units definition:
Rotational speed: N = 0.5 s⁻¹ (converted from 30.0 rpm)
Dynamic viscosity: μ = 8.0 Pa·s (converted from 8000.0 cP)
The diameter and density are already in SI units.
Calculate the Reynolds number (Re) to confirm the flow regime using Re = \( \frac{\rho N D^2}{\mu} \):
Re = \( \frac{1050.0 \times 0.5 \times (0.6)^2}{8.0} \) = 23.625.
The calculated Re = 23.625, which is within the laminar range (Re ≤ 30), validating the use of the laminar power correlation.
Compute the shaft power (P) using the laminar formula P = Kp μ N² D³, with the anchor constant Kp = 200.0:
P = 200.0 × 8.0 × (0.5)² × (0.6)³ = 86.4 W.
Apply a transmission margin for motor sizing. The margin factor is 1.25 (25%):
Power with margin, P_with_margin = 86.4 × 1.25 = 108.0 W.
Final Answer
The required shaft power for the anchor impeller is 86.4 W. After accounting for transmission losses, the motor should be sized for at least 108.0 W.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
