Which variable in the lift equation is dimensionless?

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Multiple Choice

Which variable in the lift equation is dimensionless?

Explanation:
The dimensionless quantity is the coefficient of lift, Cl. It’s defined as Cl = L / (0.5 ρ v^2 S). The numerator is lift (a force), and the denominator is dynamic pressure 0.5 ρ v^2 times the wing area S, which also yields a force. Since both numerator and denominator are in newtons, their units cancel, leaving a pure number. The other variables carry units: lift is a force, density is kg/m^3, velocity is m/s, and area is m^2. Cl acts as a pure scaling factor that depends on angle of attack and wing shape, not on the units used.

The dimensionless quantity is the coefficient of lift, Cl. It’s defined as Cl = L / (0.5 ρ v^2 S). The numerator is lift (a force), and the denominator is dynamic pressure 0.5 ρ v^2 times the wing area S, which also yields a force. Since both numerator and denominator are in newtons, their units cancel, leaving a pure number. The other variables carry units: lift is a force, density is kg/m^3, velocity is m/s, and area is m^2. Cl acts as a pure scaling factor that depends on angle of attack and wing shape, not on the units used.

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