Water Treatment Engineering, Rapid Mix & Tapered Flocculation
Camp-Stein Velocity Gradient (G) & Camp Number (Gt) Formula
Calculate Flocculation Basin RMS Velocity Gradient G (s^-1), Detention Time t (seconds), Dimensionless Camp Number G*t, and Specific Mixing Power Input (W/m³).
Cold winter water boosts viscosity mu—requiring VFD paddle speed increases to hold G = SQRT(P/(mu*V))!
Thomas Camp and P.C. Stein (1943) proved that orthokinetic particle collision frequency in water-treatment rapid-mix (G = 600–1,000 s^-1) and tapered flocculation basins (G = 70 -> 40 -> 20 s^-1; dimensionless Camp Number G * t = 20,000–100,000) is governed by the Root-Mean-Square Velocity Gradient G = SQRT(P_watts / (mu_Pa_s * V_m3))! Because dynamic water viscosity mu jumps +44% when water cools from 20°C (0.00100 Pa·s) to ~7°C winter runoff (0.00144 Pa·s), keeping constant paddle-wheel power P drops G by ~17% unless variable-frequency drives (VFDs) ramp impeller torque!
Verify on a 500 m³ Tapered Flocculation Stage—Shaft_Fluid_Power P = 450.0 W (B2), Dynamic_Viscosity mu = 0.00100 Pa·s (@ 20°C, B3), Basin_Volume V = 500.0 m³ (B4 -> Specific Power = 450 / 500 = 0.90 W/m³ in E5), and Water_Flow Q = 25.0 m³/min (B5 -> Detention Time t = (500 / 25) * 60 = 1,200.00 s in E3): Camp-Stein Velocity Gradient G equals SQRT(450 / (0.001 * 500)) = 30.00 s^-1 (E2), and Dimensionless Camp Number G * t hits 30.00 * 1,200 = 36,000.00 (E4)!
| Camp-Stein Flocculator KPI (P = 450 W, mu = 0.001 Pa·s, V = 500 m³, Q = 25 m³/min) | Formula | Verified Output |
|---|---|---|
| RMS Velocity Gradient G (s^-1) | SQRT(Power_W / (Viscosity_Pa_s * Vol_m3)) | 30.00 s^-1 (25.00 @ 7°C Winter) |
| Basin Residence Time t (sec) | (Basin_Volume_m3 / Flow_m3_min) * 60 | 1,200.00 s |
| Dimensionless Camp Number (G*t) | Velocity_Gradient_G * Residence_Time_s | 36,000.00 (30,000.00 @ 7°C) |
| Specific Mixing Power (W/m³) | Fluid_Power_W / Basin_Volume_m3 | 0.90 W/m³ |
Camp-Stein Velocity Gradient & Camp Number Formula
Validate Power_W > 0, Viscosity_Pa_s in [0.0002, 0.01], Volume_m3 > 0, and Flow_m3_min > 0!
=LET(pw_w, B2, mu_w, B3, vl_m, B4, q_mn, B5, IF(OR(pw_w <= 0, mu_w < 0.0002, mu_w > 0.01, vl_m <= 0, q_mn <= 0), "Invalid Flocculator Input", LET(g_sc, SQRT(pw_w / (mu_w * vl_m)), t_sc, (vl_m / q_mn) * 60, ROUND(g_sc * t_sc, 2))))Winter Cold-Water Viscosity Drop Check (Set Viscosity mu = 0.00144 Pa·s)
Increase Dynamic_Viscosity B3 from 0.00100 Pa·s (20°C) to 0.00144 Pa·s (7°C winter river water) at constant 450 W shaft power: Velocity Gradient G E2 drops from 30.00 s^-1 to 25.00 s^-1 and Camp Number G*t E4 falls from 36,000.00 to 30,000.00!
=IF(ISTEXT(E4), E4, ROUND(B2 / B4, 2))Try the example
Use the original values or change them to test your understanding.