**Plume Length for Steady One-Dimensional Transport**

c = concentration [m/L

^{-3}
]

t = time [T]

x = distance [L]

D = dispersion constant [L

^{2}
/T]

v = seepage velocity [L/T]

λ = first order decay constant [1/T]

**with the initial and boundary conditions**

Has the solution (rearranged for length, x):

where the dispersion coeffeicient D, has been separated into a dispersivity, α and the seepage velocity v, and

c
_{L}
is the concentration that defines the plume length.

*i.e.*, to find the distance (plume length) to the 0.02 mg/L contour, c
_{L}
is set to 0.02.

Allowing for the dispersivity to be a function of x, *f(x)*:

The calculator has three options for *f(x)*:

- Fixed Dispersivity
- One-tenth the plume Length
- Xu and Eckstien (1995) regression relation for plume length (L
_{p}
= x):