Reaeration By Fickian Diffusion

The user defines the reaeration rate at 20$\degree$C. The reaeration rate is adjusted to the local water temperature using the relationship:

$\kappa_2=\kappa_{2,20}*1.024^{(T_{water}-20)}$ 7:3.5.4

where $\kappa_2$ is the reaeration rate (day$^{-1}$ or hr$^{-1}$), $\kappa_{2,20}$ is the reaeration rate at 20$\degree$C (day$^{-1}$ or hr$^{-1}$), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C).

Numerous methods have been developed to calculate the reaeration rate at 20$\degree$C, $\kappa_{2,20}$. A few of the methods are listed below. Brown and Barnwell (1987) provide additional methods.

Using field measurements, Churchill, Elmore and Buckingham (1962) derived the relationship:

7:3.5.5

where is the reaeration rate at 20C (day), is the average stream velocity (m/s), and is the average stream depth (m).

O’Connor and Dobbins (1958) incorporated stream turbulence characteristics into the equations they developed. For streams with low velocities and isotropic conditions,

7:3.5.6

where is the reaeration rate at 20C (day), is the molecular diffusion coefficient (m/day), is the average stream velocity (m/s), and is the average stream depth (m). For streams with high velocities and nonisotropic conditions,

7:3.5.7

where is the reaeration rate at 20C (day), is the molecular diffusion coefficient (m/day), is the slope of the streambed (m/m), and is the average stream depth (m). The molecular diffusion coefficient is calculated

7:3.5.8

where is the molecular diffusion coefficient (m/day), and is the average water temperature (C).

Owens et al. (1964) developed an equation to determine the reaeration rate for shallow, fast moving streams where the stream depth is 0.1 to 3.4 m and the velocity is 0.03 to 1.5 m/s.

7:3.5.9

where is the reaeration rate at 20C (day), is the average stream velocity (m/s), and is the average stream depth (m).