Engelund-Hansen

The Engelund-Hansen (1967) formula is a total-load transport potential formula based on stream power. The formula is most appropriate for environments with uniform sediments and dominated by suspended load. The formula has been modified here for multiple grain classes and to include a critical shear stress for sediment transport as

1)

$\begin{array}{l}q_{tk}^{*}=\begin{cases} 0.05\eta _{k}\rho _{sk}U^{2}\sqrt{\frac{d_{k}}{gR_{k}}}\left(\frac{\tau _{b}}{g\left(\rho _{sk}-\rho _{w}\right)d_{k}}\right)^{3/2}\,\,\,\mathrm{for}\,\,\tau _{b}>\tau _{crk}\\ 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \end{cases}\right.\end{array}$

where

$\begin{array}{l}{q_{tk}}^*\end{array}$ = sediment transport capacity [M/L/T]

$\begin{array}{l}τ_{b}\end{array}$ = bed shear stress [M/L/T²]

$\begin{array}{l}τ_{crk}\end{array}$ = critical shear stress [M/L/T²]

$\begin{array}{l}U\end{array}$ = current velocity magnitude [L/T]

$\begin{array}{l}R_{k}\end{array}$ = $\begin{array}{l}ρ_{sk}/ρ_w− 1\end{array}$ = submerged specific gravity of a particle [-]

$\begin{array}{l}ρ_{sk}\end{array}$ = sediment density [M/L³]

$\begin{array}{l}ρ_{w}\end{array}$ = water density [M/L³]

$\begin{array}{l}d_{k}\end{array}$ = grain class diameter [L]

The suggested applicability of the Engelund-Hansen formula is for $\sqrt{d_{75}/d_{25}}$<1.6 and d₅₀<0.15 mm. It is noted that the Engelund-Hansen formula does not include a critical threshold for transport. England Hansen is the simplest transport equations. Application should be restricted to sand systems.