Can drag force and lift force be in the same direction here:

[Roul]

In the attached picture, can I say that there is a lift force in the Y-direction, and a drag force too in the same Y-direction?

F_L proportional to V_fx² ?

F_D proportional to V_py² ?

Is this equation of motion for the Y-direction correct here: ma = − mg − F_D + V(rho)g + F_L

The lift force is because of the horizontal flow which is in fact lifting the particle (lets assume there is some small velocity gradient around the particle, as the particle bottom experiences zero flow velocity and particle top experiences the flow velocity), and the drag force is due to the resistance to the particle's upward motion. Is this correct to say?

Please assume that the picture is correct, and such an observation was made.

Edit: Just added the image.
https://imgur.com/x099TgP

https://imgur.com/x099TgP

https://imgur.com/x099TgP

 

[A.T.]

can I say that there is a lift force in the Y-direction, and a drag force too in the same Y-direction?

Lift and drag are perpendicular to each other, but can both have a positive Y-component.

 

[Roul]

Lift and drag are perpendicular to each other, but can both have a positive Y-component.

So the lift force will be in the Y-direction, but the drag force will be at an angle (say theta) to the vertical direction, in between the horizontal flow velocity and the vertical particle velocity. So in my equation can I use F_L and F_Dcos(theta) and rest will be the same, right?

 

[A.T.]

So the lift force will be in the Y-direction, but the drag force will be at an angle (say theta) to the vertical direction,

Lift and drag components are perpendicular to each other per definition. Their orientation depends on what you consider as the reference flow direction.

 

[CWatters]

+1

Air flowing past an object exerts a force F acting on the object. You can resolve that force F into two components acting in any direction you want - provided the vector sum equals F. It's conventional to resolve it into two forces one acting perpendicular to the flow (lift) and one parallel to the flow (drag) but there is nothing that says you must do it that way.

For example consider a glider soaring in air flowing up a hill. You could define lift as the component acting perpendicular to the air flow or in a direction that opposes gravity. Depends what you are interested in.

 

[David Lewis]

In aeronautical engineering, lift is the aerodynamic force perpendicular to the relative wind, whereas in everyday vernacular, the term lift applies to any force that points up.