Fluid Calculations

How to Calculate Tank Volume, Blend Time, Mixer Power, and Pressure Drop in Process Plants

The five formulas process engineers run daily, solved with real inputs, units, and worked numbers from tank sizing to pressure drop.

Start with tank working volume, since it drives batch size and every downstream number. A vertical cylindrical tank has geometric volume V = pi/4 x D squared x H. For a 2.4 m diameter, 3.0 m straight-side tank, that is 0.7854 x 5.76 x 3.0 = 13.57 cubic meters, or 13,570 liters. But you never fill to the brim. Subtract freeboard, typically 10 to 15 percent, and any dead volume below the outlet or agitator. At 12 percent freeboard the Tank Working Volume calculator returns about 11,940 liters usable. Always quote working volume, not geometric, when you size a batch.

Fill and drain times set your changeover schedule. Fill time is simply working volume divided by feed rate: 11,940 L at a 150 L/min pump gives 79.6 minutes. The Tank Fill Time calculator handles this directly. Drain time by gravity is not linear because head falls as the tank empties. Using Torricelli, the theoretical empty time for a tank draining through an outlet of area a is t = (A_tank / (Cd x a)) x sqrt(2H/g). For that tank with a 50 mm outlet, Cd near 0.61, and H = 2.64 m, Tank Empty Time returns roughly 22 minutes versus a naive 8 minutes if you ignored falling head.

Batch blend time tells you when a mix is homogeneous. The common correlation is blend time theta_95 = 5.2 / (N x (D/T) squared to the 2/3 power) for turbulent flow, but the practical form most operators use is theta = k / N, where N is impeller speed in rev/s and k is a geometry constant from the impeller vendor, often 30 to 50. At N = 2 rev/s (120 rpm) and k = 40, theta = 20 seconds per pass, and you target 5 to 8 turnovers, so 100 to 160 seconds. The Batch Mixing Time calculator lets you enter impeller diameter, tank diameter, and speed rather than guessing k.

Mixer power draw sizes the motor and the electrical bill. Turbulent power is P = Np x rho x N cubed x D to the fifth, where Np is the power number (about 5.0 for a Rushton turbine, 0.3 to 1.5 for hydrofoils), rho is density in kg per cubic meter, N in rev/s, and D in meters. For a 0.8 m Rushton at 2 rev/s in water (rho 1000): P = 5.0 x 1000 x 8 x 0.328 = 13,100 W, about 13.1 kW. Raise density to 1200 for a slurry and power scales linearly to 15.7 kW. The Mixer Power Load calculator runs this and adds a gearbox and service factor margin.

Agitator tip speed is the shear proxy that protects shear-sensitive products. Tip speed = pi x D x N. That same 0.8 m impeller at 2 rev/s gives 3.14 x 0.8 x 2 = 5.03 m/s. For low-shear work like flocculation, keep tip speed under 2.5 m/s; for dispersion or emulsification you may push 8 to 20 m/s. The Agitator Tip Speed calculator flips the relationship so you can back-solve the max rpm for a shear limit: for a 5 m/s ceiling on that 0.8 m impeller, N_max = 5 / (pi x 0.8) = 1.99 rev/s, or 119 rpm.

Line sizing rests on process flow rate and velocity. Flow rate Q = V_velocity x A, where A = pi/4 x d squared. To move 150 L/min (0.0025 cubic meters per second) at a target 1.5 m/s, required area is 0.00167 square meters, so d = sqrt(4A/pi) = 46 mm, meaning you pick the next standard size up, DN50. The Process Flow Rate calculator converts between L/min, cubic meters per hour, and GPM so you stop making unit-conversion errors. Keep liquid line velocity at 1 to 3 m/s: below 1 you risk settling, above 3 you spike pressure drop and erosion.

Pressure drop decides pump head. The Darcy-Weisbach equation is dP = f x (L/d) x (rho x v squared / 2). For 50 m of DN50 pipe (d = 0.05 m) at v = 1.5 m/s in water, with friction factor f near 0.025: dP = 0.025 x (50/0.05) x (1000 x 2.25 / 2) = 0.025 x 1000 x 1125 = 28,100 Pa, about 0.28 bar or 2.9 m of head. Add fitting losses using equivalent lengths (a standard elbow adds roughly 30 pipe diameters, so 1.5 m each here). The Pressure Drop calculator sums straight run and fittings so you specify the pump correctly.

Chain the numbers to size a run end to end. Working volume 11,940 L feeds fill time 79.6 min, blend time about 150 s, mixer load 13.1 kW, and a DN50 line at 0.28 bar drop over the batch transfer. Pump runtime for the transfer is volume divided by rate, 11,940 / 150 = 79.6 min, and the Pump Runtime calculator ties that to duty cycle. Carry units through every step: mixing L, mm, rev/s, and Pa without a single feet-to-meter or rpm-to-rev/s slip is what separates a design that runs from one that trips on the first batch.

Published 2026-07-01.