# Is drag force in the direction of particle motion or opposite to motion?

Suppose water is flowing in horizontal direction (positive $x$-direction) and a particle immersed in that water is also moving in the same direction.

In this case, is the drag force $F_D$ in the direction of particle motion or opposite to it?

I get from wikipedia that drag force is a frictional force and hence is opposite to particle motion, but then what is the force that is making the particle move. Because in one journal paper, I see that drag force $F_D$ is shown as force in the direction of particle motion.

This is a sketch from the paper, you can see that flow velocity and drag force are both in the same direction.

Drag force opposes the motion of a body relative to the surrounding fluid. In this case the surrounding fluid moves to the right and relative to that the solids move to the left.

The drag force is opposing the motion to the left, hence it is towards the right. The solids are being swept away by the fluid.

• Hi thanks, this was really helpful. So can I say that force on the particle in the flow direction is proportional to $u_f^2$, and the force opposite to the motion is proportional to $u_p^2$, and since the particle is in fact moving with the flow, the net force is proportional to $(u_f-u_p)^2$ where $u_f$ = flow velocity and $u_p$ = particle velocity. So there is force in both directions, but net force is in flow direction if the particle is moving in the flow direction. – user2617526 May 2 '16 at 4:39

Motion is a very diffuse concept :) you have to add a frame of reference to make it meaningfull.

In the frame of reference of the surrounding water the force definitely tries to stop the particle.

So if you have a stone rolled along the ground by a swift stream, the force goes in the direction of motion (in the usual, external, frame of reference), since the stone is still too slow for the water; whereas for a stone falling into a deep pond, the friction will be opposite ist motion.

• hi, thanks for your quick reply. so in the above sketch, if the drag force is in the direction of motion, then what is the fluid resistance force on the particle opposite to the motion. can u give equations for these 2 forces. – user2617526 May 1 '16 at 10:54
• no, sorry, there is no simple formula for the resistance in a fluid, this is a part of physics which is (comparably) ill understood, and the equations for this kind of forces are complicated and approximate. But I think your question has still some misunderstanding - there is no resistance from the fluid and drag force - this is the same (not just equal - the same!). If I understand your picture correctly, then the force from the fluid drags sprehe1 to the right whereas the force from the ground (sprehe3) tries to stop it. – Ilja May 1 '16 at 16:36

The frictional forces try and reduce the relative motion between the water and the spheres.

If the water is travelling faster than the spheres then the water exerts a frictional force on the spheres to try to make the spheres move faster and the spheres exert a frictional force on the water to try and make the water move slower.

## protected by Qmechanic♦May 1 '16 at 18:03

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