Yang (1979; 1984) developed a total sediment transport method based on the regression of potential energy dissipation per unit weight of water and the total sediment concentration:

1) \log _{10}\left(C_{tk}^{*}\right)=\left\{\begin{array} M+N\log _{10}\left[\frac{S_{f}}{\omega _{sk}}\left(U-U_{crk}\right)\right]\,\,\,\,\mathrm{for}\,\,U>U_{crk}\,\,\\ 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \end{array}\right.
2) M=\left\{\begin{array} 5.435-0.286\log _{10}\left(\frac{\omega _{sk}d_{k}}{\nu }\right)-0.457\log _{10}\left(\frac{u_{*}}{\omega _{sk}}\right)\,\,\,\mathrm{for}\,\,d_{k}<2\,\mathrm{mm}\\ 6.681-0.681\log _{10}\left(\frac{\omega _{sk}d_{k}}{\nu }\right)-4.816\log _{10}\left(\frac{u_{*}}{\omega _{sk}}\right)\,\,\,\mathrm{for}\,\,2\,\mathrm{mm}<d_{k}<10\,\mathrm{mm} \end{array}\right.
3) N=\left\{\begin{array} 1.799-0.409\log _{10}\left(\frac{\omega _{sk}d_{k}}{\nu }\right)-0.314\log _{10}\left(\frac{u_{*}}{\omega _{sk}}\right)\,\,\,\,\mathrm{for}\,\,d_{k}<2\,\mathrm{mm}\\ 2.784-0.305\log _{10}\left(\frac{\omega _{k}d_{k}}{\nu }\right)-0.282\log _{10}\left(\frac{u_{*}}{\omega _{sk}}\right)\,\,\,\,\mathrm{for}\,\,2\,\mathrm{mm}<d_{k}<10\,\mathrm{mm} \end{array}\right.

where

{C_{tk}}^* = sediment concentration in parts per million (ppm) by weight

u_{*} = bed shear velocity [L/T]

ω_{sk} = sediment fall velocity [L/T]

ν = kinematic water viscosity [L2/T]

U = depth-averaged current velocity [L/T]

U_{crk} = critical depth-averaged current velocity [L/T]

S_{f} = friction slope [-]

The Yang (1973) transport equations tend to overestimate transport for very coarse sands and there is also a sharp discontinuity between sand and gravel at ds = 2 mm.