The chemical sulfur hexafluoride (SF_6) has been used by numerous researchers in

Question

The chemical sulfur hexafluoride (SF_6) has been used by numerous researchers instead of fluorescent dyes to study dispersion, since it is inexpensive and easily analyzed on a gas chromatograph. Clark ct at. (1996, 1997) used SF_6 as a conservative tracer in an experiment in the Hudson River and found that the longitudinal dispersion coefficient increased from 23 plusminus 3 to 78 plusminus 17 m^2 s^-1 as the chemical plume increased in size. Typical transverse mixing coefficients for this river are 0.2 m^2 s^-1'. Assuming average river conditions of a cross-sectional area of 3000 m^2, flow of 210 m^3 s^-1 and depth of 5.5 m, calculate a transverse mixing (E_4) and longitudinal dispersion coefficient (E_L) for this river.

Explanation / Answer

given that,

longitudinal dispersion coefficient varies from = 23+-3 to 78+-17 m^2/s

traverse mixing coefficients = 0.2 m^2/s

cross section area = 3000 m^2

flow = 210 m^3/s

depth = 5.5 m

traverse mixing for hudson river Et= 0.15Ush*h

where Ush = shear stress = 0.152

h = depth in m

Et = 0.2*0.152*5.5 = 0.1654 m^2/s

longitudinal disperssion coefficient El= (0.011*u^2*w^2)/(Ush*h)

El= (0.011*0.27^2*48.8^2)/(0.0191*5.5) = 1.90968/0.105 = 18.178 m^2/s.

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