Unformatted text preview: stationary so that u cv = u , letting ρ denote cup number density, the Reynolds Transport Theorem tells us that dN dt = d dt 888 V ρ dV + 8 s 8 S ρ u · n dS By definition of ρ , necessarily N cup = $$$ ρ dV . Also, the net flux of cups out of the control volume is 8 s 8 S ρ u · n dS = ˙ n sold + ˙ n stolen Now, the rate of change of the number of cups in the system is the rate at which cups are broken so that dN/dt = λ dN cup /dt , where λ = 0 . 05 = 1 / 20 . So, our basic conservation law is λ dN cup dt = dN cup dt + ˙ n sold + ˙ n stolen Since we are given ˙ n stolen = α ˙ n sold , we find (1 − λ ) dN cup dt = − (1 + α ) ˙ n sold Therefore, dN cup dt = − w 1 + α 1 − λ W ˙ n sold Finally, since α = 1 / 10 and λ = 1 / 20 , we conclude that dN cup dt = − X 11 / 10 19 / 20 ~ ˙ n sold = − 22 19 ˙ n sold...
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 Spring '06
 Phares
 Reynolds Transport Theorem, unbroken cups

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