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The science
How UV disinfects
254 nm light is absorbed by microbial DNA and blocks replication. The inactivation depends on the dose (fluence), the fluence rate integrated along each particle's path: D = ∫ E dt in mJ/cm2. Published dose-response tables (US EPA UV Disinfection Guidance Manual, 2006) give the log inactivation: for example 12 mJ/cm2 for 3-log Cryptosporidium, 7.7 for Giardia and 143 for adenovirus. The model interpolates those tables; the E. coli curve is a simple illustrative D10 of 3 mJ/cm2.
Fluence rate around a lamp
For a long lamp of arc length La and UV output P, the fluence rate at distance ρ from the axis is E = P exp(-α(ρ - r0)) / (2π ρ La) with the absorption coefficient α = -ln(UVT/100) / 1 cm (UVT = transmittance per cm). Several lamps simply add. The 1/ρ geometric term and the exponential Beer-Lambert term together make the water near the wall and between distant lamps receive much less dose.
Lagrangian dose
1500 particles are tracked through the 1.4 m vessel with a 1/7-power axial velocity profile and turbulent radial mixing (eddy diffusivity 0.067 u* R, u* = 0.061 U). Each particle accumulates its own dose. Because inactivation is a log-law, the reactor credit is LI = -log10( mean(10-f(Di)) ), always below f(mean dose): under-dosed particles cost more than over-dosed ones give. The reduction-equivalent dose (RED) is the dose that would give the same credit with perfect mixing.
Lamps, fouling and energy
UV output = electrical x 0.35 x 0.4 (sleeve, end effects, derating) x power setting x ageing (down to 75 % at 12 000 h) x sleeve transmission. Sleeve fouling grows with iron and hardness and with low UVT; wipers restore it. Electrical energy per order is EEO = Pel / (Q LI). Auto dimming lowers the power until the RED is 110 % of the requirement.
Honest simplifications
Infinite-line-source optics (no end effects or wall reflection, absorbed in the derating factor), a single dose-response curve per organism with no shoulder or tailing, no particle shading, no polychromatic spectrum, no hydraulics from inlet bends. Lamp ageing is accelerated 20 times for demonstration. Not a validated reactor design.