Engineering & Fluid Mechanics
Kynch & Talmage-Fitch Thickener Sizing Formula: Unit Area (UA) & Clarifier Diameter
Scale 1-liter graduated-cylinder hindered settling tests up to continuous industrial gravity thickeners using G. J. Kynch & Talmage-Fitch Unit Area UA = t_u / (C_0 * H_0) and tank diameter D = SQRT(4 * F * UA / pi).
From a single batch settling cylinder curve to a continuous 18-meter gravity thickener!
G. J. Kynch (1952, Transactions of the Faraday Society) proved via kinematic wave theory that in hindered batch sedimentation where settling velocity depends solely on local solids concentration v = f(C), upward-propagating concentration characteristics are straight lines from the cylinder base! William P. Talmage and E. B. Fitch (1955, Industrial & Engineering Chemistry) used Kynch’s theorem to determine the critical underflow time t_u on a single batch interface height H(t) curve!
Given initial slurry solids concentration C_0 (tonnes dry solids / m^3 slurry), initial cylinder slurry height H_0 (m), and critical underflow compression time t_u (days), the required continuous thickener Unit Area is UA = t_u / (C_0 * H_0) in m^2 / (tonne/day), and required circular tank diameter for dry solids feed rate F (tonnes/day) is D = SQRT((4 * F * UA) / PI())! For C_0 = 0.080 t/m^3, H_0 = 1.20 m, t_u = 0.16 days (3.84 hr), and F = 150 t/d, UA = 1.6667 m^2/(t/d) and D = 17.84 m (scaling to 25.23 m at F = 300 t/d)!
| Continuous Thickener Duty (UA = 1.6667 m²·d/t) | Required Thickener Area A = F*UA | Circular Tank Diameter D (m) |
|---|---|---|
| Solids Throughput F = 150 tonnes/day | 250.0 m² | 17.84 m |
| Doubled Plant Capacity F = 300 tonnes/day | 500.0 m² | 25.23 m (SQRT(2) scaling) |
| Zero Slurry Concentration C_0 = 0 | Division by Zero | "Invalid Thickener Settling Test" |
Talmage-Fitch / Kynch Specific Thickener Unit Area UA = t_u / (C_0 * H_0)
Computes required thickener settling area per unit solids throughput (m² per t/d) from initial concentration C_0 (B2, t/m³), cylinder height H_0 (B3, m), and critical underflow time t_u (B4, days).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Thickener Settling Test", ROUND(B4 / (B2 * B3), 4))Circular Gravity Thickener Diameter D (m) = SQRT((4 * F * UA) / PI())
Sizes the continuous circular thickener diameter in meters for solids feed rate F (B5, tonnes/day).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Thickener Settling Test", ROUND(SQRT((4 * B5 * (B4 / (B2 * B3))) / PI()), 2))Try the example
Use the original values or change them to test your understanding.