Agitator Design Calculation: Motor Power, Torque & Impeller Sizing

An agitator design calculation Excel worksheet should connect impeller geometry, rotational speed, liquid properties, absorbed power, and shaft torque. For a selected impeller, calculate mixing Reynolds number, obtain the applicable power number, and use P = N_pρN³D⁵. Then calculate running torque and account for transmission losses before screening a motor.

This guide works through a single-impeller blending example. A 0.60 m impeller at 180 rpm draws an estimated 2.73 kW and develops 144.8 N·m of hydrodynamic running torque. With an illustrative 90% mechanical transmission efficiency and 25% power allowance, the motor-output screening requirement becomes 3.79 kW.

These calculations estimate load; they do not prove blending time, solids suspension, dispersion quality, or mechanical suitability. The power number and operating assumptions must match the actual impeller and vessel.

Start with the mixing objective

Agitator design begins with the process result required, rather than a motor rating. A blend tank may need a specified concentration uniformity within a given time. A slurry vessel may need off-bottom suspension. A gas–liquid reactor may need mass-transfer performance. Each objective can favor a different impeller, speed, clearance, or number of impellers.

Duty	Key design questions
Liquid blending	What mixing time and uniformity are required? Are the liquids miscible?
Solids suspension	What particle sizes, densities, loading, and suspension criterion apply?
Gas dispersion	What gas rate and mass-transfer target apply? Is flooding possible?
Heat transfer	What circulation is needed near the jacket, coils, or heat-transfer surface?
Viscous processing	How does rheology change with shear, temperature, and batch progress?

For an overview of equipment options, see our agitator types and applications guide. Treat fluid allocation, tank internals, baffles, and feed location as part of the mixing system.

Essential agitator design equations

Use rotational speed in revolutions per second in the power and Reynolds-number equations:

N = n/60, where n is rpm.

Re_mix = ρND²/μ

P_impeller = N_pρN³D⁵

τ = P_impeller/(2πN)

Tip speed = πDN

Symbol	Meaning	SI unit
ρ	Liquid density	kg/m³
μ	Dynamic viscosity	Pa·s
D	Impeller diameter	m
N	Impeller rotational frequency	s⁻¹, revolutions per second
Np	Power number	Dimensionless
P	Power transferred by the impeller to the liquid	W
τ	Hydrodynamic torque at impeller speed	N·m

The units of ρN³D⁵ reduce to kg·m²/s³, or watts. Entering rpm directly in place of N would multiply the calculated power by 60³, making the result unusable.

The manufacturer’s SPX FLOW Lightnin mixing-technology brochure presents power, pumping, and impeller Reynolds-number relationships. Its emphasis on both power and flow performance is useful: equal power does not guarantee equal mixing performance.

Power number is an input that needs evidence

N_p depends on impeller geometry and the operating flow regime, as well as relevant vessel conditions. Blade count, blade angle, diameter ratio, bottom clearance, baffling, and interactions with other impellers can matter. A generic label such as “pitched-blade turbine” is not sufficient to establish a final design value.

Use a vendor curve or a suitable published correlation for the actual arrangement. In an appropriate fully turbulent regime, the curve may approach a nearly constant power number. In laminar mixing, a relation of the form N_p = K/Re may apply for a particular geometry; substitution gives P = KμN²D³. The constant K must come from relevant data.

Do not reuse pipe-flow Reynolds thresholds for a mixing tank. Nor should a single viscosity value be treated as proof of turbulence. The Sumitomo Heavy Industries mixing discussion explains why the N_p–Re relationship matters when interpreting changes in power and flow.

The example below assumes N_p = 1.30 is applicable at the calculated Reynolds number for the selected baffled arrangement. It is an illustrative coefficient, not certified performance data for a named impeller.

Worked example: blending a Newtonian liquid

Consider a vertical, baffled tank containing a single Newtonian liquid. The trial design uses one submerged impeller and no gas sparging. Density and viscosity are treated as constant, and the operating objective is bulk blending. No blend-time guarantee is assigned.

Input	Illustrative value
Tank inside diameter T	1.80 m
Cylindrical liquid height H	1.80 m
Impeller diameter D	0.60 m
Impeller speed n	180 rpm
Liquid density ρ	1,000 kg/m³
Dynamic viscosity μ	0.010 Pa·s = 10 cP
Assumed applicable power number	1.30
Mechanical transmission efficiency ηmech	0.90
Illustrative power allowance multiplier M	1.25

The cylindrical volume excludes dished-head volume and internals displacement. Use actual working volume for a real vessel. The trial ratio D/T = 0.333 is a geometry choice for this example, not a universal impeller-sizing rule.

Step 1: Calculate volume and speed

V = πT²H/4 = π × 1.80² × 1.80/4 = 4.580 m³

N = 180/60 = 3.00 s⁻¹

Use the agitator output speed after the gearbox. The motor rotor speed is generally different and must not be substituted into the impeller equations.

Step 2: Calculate impeller Reynolds number

Re_mix = 1000 × 3.00 × 0.60²/0.010 = 108,000

This is consistent with using a turbulent-region coefficient for many conventional baffled impellers, but the selected impeller’s curve remains the basis for accepting N_p = 1.30. If viscosity rises during the batch, recalculate Reynolds number and revisit the coefficient.

Step 3: Calculate absorbed impeller power

P = 1.30 × 1000 × 3.00³ × 0.60⁵ = 2729.38 W = 2.729 kW

This is the estimated power delivered to the liquid by the impeller. It excludes losses upstream of the impeller and is not the same as the electrical power measured at the motor supply.

Step 4: Calculate running torque and tip speed

τ = 2729.38/(2π × 3.00) = 144.8 N·m

An equivalent practical expression is τ ≈ 9550 × P(kW)/n(rpm). Use power and speed at the same shaft location.

Tip speed = π × 0.60 × 3.00 = 5.655 m/s

Tip speed can help compare mechanical and shear-related operating conditions. It does not independently predict local shear rate, droplet size, or damage to a shear-sensitive product.

Step 5: Calculate power per working volume

P/V = 2.729/4.580 = 0.596 kW/m³

Record this as a comparison metric, not an acceptance limit. A tank can have adequate average power per volume and still contain stagnant regions or fail to suspend solids because the circulation pattern is unsuitable.

From impeller power to motor and gearbox selection

For this screening calculation, the assumed 90% mechanical efficiency represents the aggregate running losses between motor output and the liquid-driving impeller. Its value must be replaced by an appropriate drive-loss estimate. If gearbox losses and seal losses are modeled separately, do not count them again inside the efficiency.

Required motor mechanical output = M × P_impeller/η_mech

Required output = 1.25 × 2.729/0.90 = 3.791 kW

A nominal 4 kW motor is therefore a candidate for further review, not an approved selection. Confirm available rating, duty, voltage, ambient conditions, hazardous-area requirements where relevant, VFD operation, and the actual speed–torque capability.

The corresponding allowance-adjusted hydrodynamic torque is 1.25 × 144.8 = 181.0 N·m. At 180 rpm, a 4 kW motor with the assumed mechanical transmission efficiency could deliver about 191.0 N·m to the impeller at rated motor output. That does not establish the gearbox’s permissible continuous or peak output torque.

The 1.25 multiplier is merely an example power allowance. It is not a calculated startup factor, a motor nameplate service factor, or a manufacturer-approved gearbox service factor. SEW-EURODRIVE’s service-factor guidance notes that the relevant determination depends on the manufacturer’s method and catalog data.

Motor efficiency is needed separately for electrical input. If an illustrative motor efficiency were 92% at the operating point, normal electrical input would be approximately 2.729/(0.90 × 0.92) = 3.296 kW, excluding VFD losses. Do not compare that electrical input directly with a motor rating specified as mechanical output.

Startup torque and mechanical integrity

Running power does not resolve breakaway or acceleration torque. A simplified shaft-referred balance includes load torque, friction, and inertial torque:

τ_required = τ_load + τ_friction + J_equivalentα

Refer every term to the same shaft, applying gearbox ratio and efficiency consistently. Cold viscous material, settled solids, or yield-stress behavior can create loads that the steady Newtonian example does not represent. At zero speed, the running relation P/(2πN) cannot be used to infer breakaway torque.

The Oriental Motor sizing guidance identifies inertia, torque, speed, and acceleration capability as separate selection checks. For an industrial agitator, also obtain the mixing vendor’s load cases and gearbox manufacturer’s continuous and peak ratings.

Shaft diameter cannot be finalized from torsion alone. Evaluate bending from hydraulic forces, fatigue, stress concentrations, bearing loads, critical speeds, deflection at the seal, impeller attachment, and mounting loads. VFD speed changes may cross a mechanical resonance even when motor power remains acceptable.

Impeller sizing: geometry and available power

One useful screening rearrangement is:

D = [P_{allowable,impeller}/(N_pρN³)]^1/5

For the candidate 4 kW motor, retaining the example efficiency and allowance:

P_{allowable,impeller} = 4000 × 0.90/1.25 = 2880 W

D = [2880/(1.30 × 1000 × 3³)]^1/5 = 0.6065 m

This is a power-budget diameter, not the required mixing diameter. The selected impeller must also satisfy circulation, submergence, bottom clearance, tank geometry, and process performance. Changing D/T may change N_p, so the rearrangement is only valid while the assumed coefficient remains applicable.

For solids handling, review our agitator design guide for preventing solids settling. A power-budget diameter cannot establish just-suspended speed without particle and geometry information.

Build the agitator calculation in Excel

Use column A for labels, B for inputs or formulas, and C for units. Keep the power-number source and its validity range in a visible note. These formulas use English function names and comma separators.

Cell	Input	Value
B2	Tank diameter, m	1.8
B3	Cylindrical liquid height, m	1.8
B4	Impeller diameter, m	0.6
B5	Impeller speed, rpm	180
B6	Density, kg/m³	1000
B7	Dynamic viscosity, Pa·s	0.010
B8	Applicable power number	1.30
B9	Mechanical efficiency	0.90
B10	Illustrative power allowance multiplier	1.25
B11	Candidate motor mechanical rating, kW	4

Cell	Output	Excel formula
B14	Working volume, m³	=PI()*B2^2*B3/4
B15	Speed, rev/s	=B5/60
B16	D/T	=B4/B2
B17	Mixing Reynolds number	=B6*B15*B4^2/B7
B18	Impeller power, W	=B8*B6*B15^3*B4^5
B19	Impeller power, kW	=B18/1000
B20	Running hydrodynamic torque, N·m	=B18/(2*PI()*B15)
B21	Tip speed, m/s	=PI()*B4*B15
B22	Power per volume, kW/m³	=B19/B14
B23	Screening motor-output requirement, kW	=B19*B10/B9
B24	Power-budget diameter, m	=((B11*1000*B9/B10)/(B8*B6*B15^3))^(1/5)
B25	Candidate power check	=IF(B11>=B23,"Meets power screen only","Below power screen")

Require positive dimensions, speed, density, viscosity, power number, and motor rating; constrain efficiency to greater than zero and no more than one. Use an allowance multiplier of at least one for this screening method. Check D < T and confirm actual impeller clearance and submergence separately.

The sheet does not automatically select N_p or certify a flow regime. Recalculate using a suitable correlation whenever speed, viscosity, or geometry changes. A zero-speed case requires separate logic for startup analysis. This article supplies a worksheet layout and formulas, not a newly generated Excel download.

Check speed and diameter sensitivity

The following results retain density = 1,000 kg/m³ and N_p = 1.30. They are conditional comparisons under that constant-power-number assumption.

Speed, rpm	Diameter, m	Power, kW	Running torque, N·m	Motor-output screen, kW
150	0.60	1.580	100.6	2.194
180	0.60	2.729	144.8	3.791
210	0.60	4.334	197.1	6.020
180	0.66	4.396	233.2	6.105

At constant diameter and power number, power varies with speed cubed and torque with speed squared. Increasing diameter by 10% increases calculated power by 1.1⁵ = 1.6105, or about 61%. The candidate 4 kW motor does not meet the example power screen for either the 210 rpm case or the 0.66 m impeller case.

Reducing speed may reduce power but also reduce circulation and mixing performance. When comparing scale-up options, constant tip speed, constant power per volume, and constant Reynolds number are different constraints. No single one automatically preserves all process outcomes.

When this simplified model needs extending

Multiple impellers require interaction and spacing review; adding isolated-impeller power values is only an approximation unless supported by data. Gas sparging can alter power draw and flow patterns. Non-Newtonian fluids require a rheology-aware approach rather than an arbitrary constant viscosity.

If impeller pumping capacity is needed, a suitable flow-number relationship is Q_p = N_qND³. Obtain N_q for the actual geometry. Tank volume divided by pumping rate is a nominal circulation timescale, not a guaranteed blend time.

Investigate unexpected motor current alongside measured speed, density, viscosity, liquid level, and mechanical condition. High current can indicate increased process load or mechanical drag. Low absorbed power can coexist with poor mixing caused by inadequate immersion, vortexing, gas effects, or damaged blades.

Frequently asked questions

1. What is the main agitator power formula?

P = N_pρN³D⁵, with N in revolutions per second and D in metres. Select the power number from data applicable to the impeller, flow regime, and tank arrangement.

2. How do I calculate agitator torque from kW and rpm?

Running torque in N·m is approximately 9550 × power in kW divided by rpm. Use power and speed at the same shaft location; startup torque requires a separate assessment.

3. Can I choose the motor directly from impeller power?

No. Account for mechanical losses and the specified operating envelope, then check startup, acceleration, gearbox ratings, motor duty, and speed–torque capability.

4. Is D/T = one-third always correct?

No. It is a trial ratio in this example. Impeller type, process objective, clearance, liquid level, and circulation requirements determine suitable geometry.

5. Can a constant power number be used for viscous liquids?

Only where the applicable N_p–Re data supports it. Laminar and transitional operation generally require a Reynolds-dependent correlation, with additional treatment for non-Newtonian rheology.

6. Does sufficient power guarantee solids suspension?

No. Particle properties, solids loading, impeller position, flow pattern, and the required suspension criterion must also be evaluated.

7. Does this Excel calculation determine shaft diameter?

No. It estimates hydrodynamic running load. Shaft design also needs bending, fatigue, deflection, critical-speed, attachment, seal, and bearing checks.

Use the worksheet to document assumptions and compare options

The example produces 2.73 kW of impeller power, 144.8 N·m of running torque, and a 3.79 kW motor-output screening requirement. Carry those results into a process-performance and mechanical review rather than treating them as a complete equipment selection. Explore more engineering calculation guides at GrowMechanical.