(1)$q_b = 8 [g(s-1)d^3]^{1/2}(\theta-\theta^b_{cr})^{3/2}$
where $$\theta$$ is the Shields parameter and $$\theta^b_{cr}$$ is the critical Shields parameter for bedload motion. In Meyer-Peter and Muller (1984), $$\theta^b_{cr} = 0.047$$.
(2)$q_b = \frac{8 [(\tau_b-\tau^b_{cr})/\rho_w]^{3/2}}{g(s-1)}$
where $$\tau^b_{cr}$$ is the critical shear stress for bedload motion which can be calculated using $$\theta^b_{cr}$$.