Problem 1.10 - Problem 1.10 [Difficulty: 4] NOTE: Drag...

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Problem 1.10 [Difficulty: 4] NOTE: Drag formula is in error: It should be: F D 3 π V d = Mg F D = 3 π Vd a = dV/dt Given: Data on sphere and formula for drag. Find: Diameter of gasoline droplets that take 1 second to fall 10 in. Solution: Use given data and data in Appendices; integrate equation of motion by separating variables. The data provided, or available in the Appendices, are: μ 4.48 10 7 × lbf s ft 2 = ρ w 1.94 slug ft 3 = SG gas 0.72 = ρ gas SG gas ρ w = ρ gas 1.40 slug ft 3 = Newton's 2nd law for the sphere (mass M) is (ignoring buoyancy effects) M dV dt Mg 3 π μ V d = dV g 3 π μ d M V dt = so Integrating twice and using limits Vt () 3 π μ d 1e 3 π μ d M t = xt 3 π μ d t M 3 π μ d e 3 π μ d M t 1 + = Replacing M with an expression involving diameter d
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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