An experiment is carried out to determine the longitudinal dispersion coefficient in a river. The experiment is started by injecting a conservative dye into the river at a certain point in such a way...

An experiment is carried out to determine the longitudinal dispersion coefficient in a river. The experiment is started by injecting a

conservative dye into the river at a certain point in such a way that full mixing across the width and depth is achieved quickly, resulting in an initial concentration C₀. The dye is added continuously over a period of 24 hours. This period of time is considered to be sufficiently long that a continuous plane source solution may be used (actually, an instantaneous volume source solution also is valid, and easier to work with). The proposed solution is

Where erfc is the complimentary error function. At a point x = 25 km downstream, the cross-sectional average dye concentration is measured as a function of time, resulting in the plot shown in Fig. 10.33.

(a) What is the governing equation for this problem? List all assumptions and any initial and boundary conditions. Is the above solution consistent with these conditions?

(b) What is the mean river velocity (U)?

(c) Estimate the longitudinal dispersion coefficient E_L.