Suppose a fluid is moving in the positive x direction and a particle immersed in that fluid is also moving in the same direction as that of the fluid, then what is the direction of drag force?
If the particle is moving exactly at the same velocity as the fluid, so the relative velocity is zero and you don't have any drag force. Otherwise if particules have a velocity Vp and the fluid a velocity Vf (Vp and Vf are 3D vectors), the direction of drag will be the direction of the relative velocity Vf-Vp. Often the particules move slowly compared to the fluid so sometimes you have ||Vp||
I should have told that I was talking about the drag force on the particle, not of the drag force your mixed fluid+particles will induce on some obstacle/vehicle (that drag force will be opposite to this mixture's mean velocity I would say)