Sedimentation Tank

What is modelled

In an ideal horizontal-flow settling tank every particle falls at its own settling velocity while the water carries it along at the flow speed. A particle that reaches the floor before the outlet is removed. All particles with a settling velocity above the overflow rate (flow divided by the floor area) are removed completely, and slower ones in proportion to their velocity. The depth of the tank does not appear.

Equations

• Overflow rate v0 = Q / (B L); removal of one size min(1, vs / v0).
• Stokes law vs = (ρp − ρw) g d2 / (18 μ), with the drag law CD = 24/Re (1 + 0.15 Re0.687) used when the Reynolds number is not small.
• Viscosity μ(T) = 2.414×10−5 · 10247.8/(T − 140) Pa s with T in kelvin.
• Total removal is the integral of the removal of one size over the log-normal size distribution.

Checks run in the page

• RK4 terminal velocity against the force-balance solution.
• The Stokes limit for a 20 micrometre particle.
• A random-particle simulation against the quadrature of the removal.
• Particle paths in a tank of twice the depth.

Honest simplifications

The tank is an ideal quiescent plug-flow basin with no turbulence, short-circuiting, scour or inlet zone, and every particle is a single sphere that does not flocculate. Real clarifiers need a safety factor, and the result is useful for the trends only.

• Press Overloaded and watch the removal fall as the overflow rate rises.
• Press Cold water: the slower viscous settling lowers the removal.
• Change the depth: the removal does not move, but the detention time does.