Tank agitation and mixing: power, Reynolds and scale-up

It works out how much power an agitator draws, its flow regime (laminar, transitional or turbulent), the motor it needs, how intense the agitation is in hp/1,000 gal, the blade tip speed, the blend time and how to scale up to a larger tank. Use it to check an existing agitator, pick speed and diameter for a new one or move a pilot recipe to production.

With P = Np · ρ · N³ · D⁵, using the impeller power number Np. First the Reynolds number, Re = ρ·N·D²/μ: in the example, a 21 in pitched-blade turbine at 150 rpm in water gives Re = 710,970, turbulent flow, where Np = 1.27 is constant. Power drawn is 1.15 hp in a 5.25 ft diameter tank with 5.25 ft of liquid (850 gal).

From McCabe, Smith and Harriott Table 9.2, for a tank with 4 baffles: Rushton turbine KT 5.75 and KL 65; 4-blade 45° pitched blade KT 1.27; marine propeller KT 0.32; HE-3 type hydrofoil KT 0.28; anchor KL 300. In laminar flow Np = KL ÷ Re; in the transition the calculator interpolates, which may be off by 30% or more. As a check, the book’s Example 9.1 (2 ft disk turbine at 90 rpm in 50% caustic) gives about 2.5 kW (3.3 hp), and the calculator 2.46 kW.

Divide power drawn by gearbox and bearing efficiency and add a margin. In the example, 1.15 hp ÷ 0.95 = 1.21 hp at the motor shaft; with 15% margin, 1.39 hp, so a standard 1.5 hp motor. If the product thickens or takes on solids during the batch, size for the worst point and check starting in the motor calculator.

The tank gets 1.35 hp/1,000 gal, in the homogeneous reaction range (0.5 to 1.5 hp/1,000 gal) from Walas’ rules of thumb. Blending needs 0.2 to 0.5; reaction with heat transfer, 1.5 to 5; gas–liquid, 5 to 10; slurries, about 10 hp/1,000 gal. These ranges are indicative: solids suspension and gas dispersion depend on the particles and gas rate, and a pilot test is worth more.

With geometric similarity every dimension grows by R = (V₂/V₁)^(1/3). For 6,500 gal, R = 1.97: the impeller becomes 41 in. Holding P/V, speed drops to 95 rpm and power rises to 8.78 hp; keeping the same speed would take about 34 hp. Constant P/V is the starting point for reaction, heat transfer and suspension; constant tip speed for shear-sensitive products.

It applies to Newtonian fluids, one centered impeller and a baffled tank; without baffles a vortex forms and actual power is lower. Blend time (17 s in the example, by the Grenville and Nienow correlation) only applies in turbulent flow with liquid height close to diameter. An agitator is rotating machinery: follow OSHA 1910.212 guarding and lockout/tagout, and treat tank entry as a permit-required confined space.