Section 378.APPENDIX A  First Order Die-off Equation

The first order die-off equation provides a method of estimating fecal coliform die-off in a receiving water as a function of time:

N_t = [N_u/(1+1/d) + N_o/(1+=d)] x e ^{-k t}

Definition and discussion of terms:

N_t is the predicted concentration of fecal coliform at travel time t

downstream; units = #/100 ml.

N_u is the fecal coliform concentration upstream of the source being

modeled; units = #/100 ml.

This term will often be negligible relative to the contribution of the

source.

N_o is the fecal coliform concentration in the effluent of the source;

units = #/100 ml.

d is the ratio of the receiving water discharge directly upstream of the

source to the discharge of the source; no units.

k is the first order die-off rate constant; units = 1/hours.  The value of

k can vary as a function of receiving water characteristics, including

temperature, exposure to sunlight, and turbidity.

t is the travel time to the point of interest below the source; units

= hours.

e = 2.718