# Relation between airespeed and pushing force

I'd like to know how can I estimate the maximum speed that can be achieved by a "portion of wind" accelerated upward from rest on the surface of a place by pushing forces.

So far I've thinking in the relation between lift and speed (for an object such as an air plane),

$Lift=\frac{1}{2}ρv^2 × C_l × area$

But not sure if I can use this expression for "a portion of air", for air moving specifically.

• when the power input is equal to the sum of the losses. May 28 '18 at 5:23
• How is the air moved? What sort of forces are moving the air?
– SF.
May 28 '18 at 12:37
• @SF. There's no info about that..only the one i give away. May 29 '18 at 16:24
• @VANESSA: Unfortunately, in this case this is unanswerable because a "pushing force" may be anything. Blades of horizontal propeller; buoyancy as the air is heated; electrostatic repulsion after ionizing the air; the entire surface moving upwards; the air being enclosed in a balloon and pushed by kid's hands; explosives going off and displacing the air with combustion products. How can we give an equation without a clue what the input variables are?
– SF.
May 29 '18 at 22:11
• I can think of three situations that would match the conditions in your questions: atmospheric thermals over land, cyclones/hurricanes or a near surface nuclear detonation.
– Fred
Jun 3 '18 at 8:56