Question

We are currently learning about drag forces and air resistance. My professor asked us to "argue to the v 2 dependence for turbulent flow by considering a falling object of cross sectional area A, speed v and mass M. Assume the air molecules have mass m, density ρ. You can then derive the force on the object in terms of A, ρ and v. " she gave us these hints:

turbulent flow formula: F = 1/2 πρCd*r^2 *v^2

Air molecules are hit by object of x-section A, speed vterm • Air molecules have mass m and density ρ • What force do they exert on the object? • NB: Newton #3 is valid...

F=ΔP/Δt ρ= m #molecues / Volume In Δt, volume swept is ΔV=A v Δt # molecules hit in Δt = ρ ΔV/m ΔP = mv * # molecules hit in Δt àF=ΔP/Δt = mv ρ ΔV/ (m Δt) = mv ρ A v Δt / (m Δt) = ρ A v2

Answer 1

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