Agitator Power Draw
Finds the shaft power an impeller draws in a baffled mixing tank, from its speed, its diameter, its type and the liquid’s density and viscosity. Process engineers use it to size an agitator motor and gearbox, or to check whether a speed change will overload the drive.
How the power is calculated
The impeller Reynolds number sets the flow regime, and the power number Np links the speed to the power [1, 2]:
Re = ρ·N·D2/μ
P = Np·ρ·N3·D5
where ρ is the liquid density, μ its dynamic viscosity, N the impeller speed in revolutions per second and D the impeller diameter. In laminar flow (Re below about 10) the power number falls as Np = KL/Re, so the power does not depend on density. In turbulent flow (Re above about 104) in a baffled tank, Np levels off at a constant Np∞. The page uses the larger of KL/Re and Np∞, which follows both lines and never lets the power drop as Re rises.
The impeller list gives KL and Np∞ from McCabe, Smith and Harriott Table 9.2 [1], for a tank with four wall baffles each one tenth of the tank diameter. Picking a liquid fills its density and viscosity [4–7].
Limits and common mistakes
- N is in revolutions per second. Divide rpm by 60.
- Power goes as D5 and N3. A 10 % error in the diameter is a 61 % error in power.
- Between Re = 10 and 104, the real power curve can lie above or below the envelope the page uses. Treat the result as an estimate there, and use the impeller maker’s curve for a close figure [3].
- The constants are for a fully baffled tank. An unbaffled tank in turbulent flow draws much less power and forms a vortex.
- Gas sparging cuts the power of a Rushton turbine sharply. Solids, non-Newtonian liquids and several impellers on one shaft also need their own corrections.
- P is the power at the impeller. Add gearbox, seal and motor losses before choosing the motor.
Worked example
A baffled tank of water at 20 °C is mixed by a 600 mm six-blade Rushton turbine at 120 rpm. What power does the impeller draw?
- Enter Impeller Rotational Speed 2 rev/s (120 rpm ÷ 60) and Impeller Diameter 600 mm.
- Choose Liquid Water, 20°C.
- Choose Impeller Type Turbine, 6-blade disk (Rushton), which fills Np∞ = 5.75 and KL = 65.
- Press Solve. The Solution shows:
Impeller Reynolds number Re: 717,269
Flow regime: Turbulent (Re > 10⁴)
Power number Np: 5.75
Shaft power P: 3,570.52 W
Shaft power P: 3.57052 kW
Check by hand. Re = 998.2 × 2 × 0.36/0.001002 ≈ 717,000, well into turbulent flow, so Np = 5.75. Then P = 5.75 × 998.2 × 8 × 0.07776 ≈ 3,571 W. At 85 % for the gearbox and motor together, that calls for about 4.2 kW from the supply, so a 5.5 kW motor fits.
