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Flocculation Calculator

Velocity gradient equals square root of power over viscosity times volume

Solution

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Velocity Gradient Equation

Calculate the velocity gradient (shear intensity) in a flocculation basin from the power input, dynamic viscosity, and tank volume. Typical G values range from 20 to 80 s⁻¹.

G = √(P / (μ × V))

Power Dissipated (Paddle)

Calculate the power dissipated by paddle mixers from the drag coefficient, paddle area, water density, and relative paddle velocity.

P = Cd × A × ρ × v³ / 2

How It Works

Flocculation gently stirs chemically treated water so that tiny destabilized particles collide and stick together into larger clumps called flocs. The velocity gradient G quantifies the shear intensity -- too low and particles rarely collide, too high and fragile flocs break apart. Designers also calculate the power needed by paddle mixers using fluid density, drag coefficient, and blade velocity. Typical G values for flocculation range from 20 to 80 s⁻¹, with detention times of 20-40 minutes, giving G×t products of roughly 10,000-100,000.

Example Problem

A flocculation tank has 150 W of power input, a volume of 50 m³, and the water viscosity is 0.001 Pa·s. What is the velocity gradient?

  1. G = √(P / (μV)) = √(150 / (0.001 × 50))
  2. G = √(3,000,000) ≈ 1,732 s⁻¹

This is well above typical flocculation ranges, suggesting the power input should be reduced or the tank enlarged.

When to Use Each Variable

  • Solve for Velocity Gradient (G) — when you know power input, viscosity, and tank volume and need to verify the mixing intensity is within the 20-80 s^-1 range for flocculation.
  • Solve for Power Input — when you have a target G value and need to size the mixer motor for a given tank volume and water viscosity.
  • Solve for Dynamic Viscosity — when you need to back-calculate viscosity from measured power and G — useful for verifying water temperature assumptions.
  • Solve for Tank Volume — when you have a fixed mixer power and target G and need to determine the required basin size.
  • Solve for Power Dissipated — when you know paddle geometry, drag coefficient, density, and velocity and need to calculate the power delivered by paddle mixers.

Key Concepts

Flocculation is the gentle mixing stage in water treatment where chemically destabilized particles collide and aggregate into larger, settleable flocs. The velocity gradient G quantifies shear intensity and is the square root of power input divided by viscosity and volume. Too little shear means insufficient collisions; too much shear breaks fragile flocs apart. The G*t product (gradient times detention time) characterizes total mixing energy, with typical values of 10,000 to 100,000 for water treatment.

Applications

  • Drinking water treatment: designing flocculation basins that precede sedimentation and filtration
  • Wastewater treatment: sizing mixing tanks for chemical phosphorus removal and coagulation
  • Industrial process water: flocculating suspended solids from cooling tower blowdown or mining wastewater
  • Stormwater management: designing detention basins with gentle mixing zones for particulate removal

Common Mistakes

  • Confusing rapid mix (G = 300-1000 s^-1) with flocculation (G = 20-80 s^-1) — the two stages have very different mixing intensities
  • Ignoring temperature effects on viscosity — cold water is more viscous, which changes G for the same power input
  • Using paddle tip speed instead of relative velocity — the effective paddle velocity is about 0.75 times the tip speed because the water moves with the paddle
  • Neglecting the G*t product — achieving the right G without adequate detention time results in poor floc formation

Frequently Asked Questions

What is the velocity gradient in flocculation?

The velocity gradient G measures the intensity of shear mixing in a flocculation basin. It is calculated as the square root of power input divided by viscosity and volume, expressed in inverse seconds. Values of 20-80 per second are typical for gentle flocculation.

What is the G times t value for flocculation?

G times t is a dimensionless product of velocity gradient and detention time that characterizes the total mixing energy applied. For water treatment flocculation, G times t typically ranges from 10,000 to 100,000 to ensure adequate particle collisions without floc breakup.

How does paddle speed affect flocculation?

Faster paddles increase the velocity gradient and collision rate, promoting rapid floc growth. However, excessive speed can shear apart delicate flocs. Paddle tip speeds are usually kept between 0.3 and 0.9 m/s in practice.

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