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Table 6 Diffusion coefficients (DL, Dy) using Empirical equations for free flow

From: Longitudinal and lateral diffusion of solute transport in flow with rigid vegetation

ReferencesEmpirical equations for free flowDiffusion coefficients (DL, Dy, cm2/s)*
Elder [32]\(D_{{_{L} }} = 5.93hu_{ * }\)341.00
Fisher [33]\(D_{L} = 0.11\left( {\frac{{w^{2} }}{h}} \right)\left( {\frac{{u^{2} }}{{u_{ * } }}} \right)\)1.72–6.89
Liu [34]\(D_{L} = \beta \frac{{w^{2} u^{2} }}{{hu_{ * } }}\beta = 0.18\left( {\frac{{u_{ * } }}{u}} \right)^{1.5}\)21.25–29.91
Seo and Cheng [35]\(D_{L} = 5.915hu_{ * } \left( {\frac{w}{h}} \right)^{0.62} \left( {\frac{u}{{u_{ * } }}} \right)^{1.428}\)76.71–206.42
Kashefipour and Falconer [36]\(D_{L} = 10.612hu\frac{u}{{u_{ * } }}\)41.52–166.07
\(D_{L} = \left[ {7.428 + 1.775\left( {\frac{w}{h}} \right)^{0.62} \left( {\frac{{u_{ * } }}{u}} \right)^{0.572} } \right]hu\frac{u}{{u_{{_{*} }} }}\)52.08–178.19
GA model [37]\(D_{L} = 2\left( {\frac{w}{h}} \right)^{0.96} \left( {\frac{u}{{u_{ * } }}} \right)^{1.25}\)41.71–99.19
Li et al. [38]\(D_{y} = 0.062\left( {\frac{w}{h}} \right)^{0.277} hu_{ * }\)4.32
Deng et al. [39]\(D_{y} = 0.16hu_{ * }\)9.12
  1. *With flume width w = 30 cm, water depth h = 15 cm, mean flow velocity u = 1−2 cm/s, friction velocity u* ≈ 3.8 cm/s