Lift force (FL) is expressed mathematically, as
- AFL = (ρU² × CL)/2
- BFL = (ρU² × CL × A)/2Correct
- CFL = 2ρU² × CL × A
- DFL = ρU² × CL × A
Solution
Concept
Mathematical formula for fluid lift force
Formula
FL = (ρ × U2 × CL × A) / 2
Step-by-step solution
1. Dynamic pressure in a fluid flow is given by (ρ × U2) / 2, where ρ is fluid density and U is flow velocity. 2. Lift force is obtained by multiplying dynamic pressure by the projected area A and coefficient of lift CL. 3. Expressed mathematically, Lift force FL = (ρ × U2 × CL × A) / 2. Answer: B
Explanation
Lift force is generated perpendicular to the direction of flow and depends on dynamic pressure, projected area, and the lift coefficient. Dynamic pressure is defined as half of density times velocity squared, which is multiplied by the lift coefficient and area. Thus, the mathematical formula for lift force is FL = (ρU² × CL × A)/2.
Why the other options are wrong
A) The formula lacks the surface area term necessary to calculate force. C) The dynamic pressure term uses 1/2, so multiplying by 2 is mathematically incorrect. D) The factor of 1/2 from the dynamic pressure term is missing.
Shortcut
Lift force equals dynamic pressure (½ ρ U²) times lift coefficient (CL) times Area (A).
Common mistake
Forgetting the 1/2 factor from dynamic pressure or omitting area from the lift force equation.
Correct answer: B) FL = (ρU² × CL × A)/2