Streeter-Phelps Equation
Calculates the oxygen deficit at any time \( t \).
\( D_t \)Oxygen deficit at time t (mg/L)
\( DO_t \)Dissolved oxygen at time t (mg/L)
\( k_d \)Deoxygenation rate (d⁻¹)
\( k_r \)Reaeration rate (d⁻¹)
\( L_a \)Ultimate BOD of mixture (mg/L)
Source: Streeter, H. W., & Phelps, E. B. (1925). A study of the pollution and natural purification of the Ohio River. US Public Health Service Bulletin No. 146.
Initial Deficit (\( D_0 \))
The deficit at the mixing point is the difference between saturation DO and initial DO.
Saturated Oxygen (\( DO_s \))
Calculated via Henry's Law constant (\( K_H \)) which varies with temperature \( T \) (Kelvin).
\( K_H^\ominus \)\( 1.3 \times 10^{-3} \) mol/(L·atm) at 298.15 K
\( C \)1700 K (temperature dependence)
\( p_{O_2} \)Partial pressure of O₂ (\( 0.2095 \times P \))
\( M_{O_2} \)Molar mass of O₂ (31.998 g/mol)
Source: Sander, R. (2015). Compilation of Henry's law constants (version 4.0). Atmospheric Chemistry and Physics, 15(8), 4399-4981.