The BBO equation, in the formulation as given by Zhu & Fan (1998, pp. 18–27) and Soo (1990), pertains to a small spherical particle of diameter having mean density whose center is located at . The particle moves with Lagrangian velocity in a fluid of density , dynamic viscosity and Eulerian velocity field . The fluid velocity field surrounding the particle consists of the undisturbed, local Eulerian velocity field plus a disturbance field – created by the presence of the particle and its motion with respect to the undisturbed field For very small particle diameter the latter is locally a constant whose value is given by the undisturbed Eulerian field evaluated at the location of the particle center, . The small particle size also implies that the disturbed flow can be found in the limit of very small Reynolds number, leading to a drag force given by Stokes' drag. Unsteadiness of the flow relative to the particle results in force contributions by added mass and the Basset force. The BBO equation states:
with the material derivative of Note that in the Navier–Stokes equations is the fluid velocity field, while, as indicated above, in the BBO equation is the velocity of the undisturbed flow as seen by an observer moving with the particle. Thus, even in steady Eulerian flow depends on time if the Eulerian field is non-uniform.