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p0464 - thugs in Spectre headquarters N is N = 888 V ρ dV...

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438 CHAPTER 4. KINEMATICS 4.64 Chapter 4, Problem 64 We can apply the Reynolds Transport Theorem to this problem if we consider the Spectre thugs to be a system and Spectre headquarters a control volume. Since the Spectre headquarters building is stationary, u rel = u . Thus, the Reynolds Transport Theorem tells us ˙ N 007 = d dt 888 V ρ dV + 8 s 8 S ρ ( u · n ) dS where ˙ N 007 is the rate at which Bond is terminating thugs and ρ is the number density of thugs, i.e., number of thugs per unit volume. Also, by definition, the number of live
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Unformatted text preview: thugs in Spectre headquarters, N , is N = 888 V ρ dV So, the Reynolds Transport Theorem simplifies to − ˙ N 007 = dN dt + 8 s 8 S ρ ( u · n ) dS = dN dt + nvA Therefore, the rate of change of live thugs in Spectre headquarters is dN dt = − ˙ N 007 − nvA Note that Agent Leiter’s arrests outside of the control volume has no impact on the rate of change of live thugs within the control volume....
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