Theory: Body force term

Hey folks,

I read somewhere, that you can introduce a body force term for simulating a pressure gradient or something like that.
You’ll have to add a term F_i to the wished directions in the collision term. In 3d Case:

F_i = rho018visc*u_f / l0 / l0 / l0 / 10

where 18 are the directions all together (without zeroth direction) ,10 are the number of directions in which the force term should act, l0 is a characteristic length scale and u_f the velocity which should be imposed.

My question: What is the theory of that formular and where do it come from?