(a) Consider a perfect fluid with density ρ, pressure P, and velocity 𝐯 that vary in time and space. Explain why the fluid's momentum density is 𝐆=ρ𝐯, and explain why its momentum flux (stress tensor) is 𝐓=P 𝐠 ρ𝐯 ⊗𝐯, or, in slot-naming index notation, Ti j=P gi j ρvi vj (b) Explain why the law of mass conservation for this fluid is (∂ρ)/(∂t) ∇·(ρ𝐯)=0 (c) Explain why the derivative operator (d)/(d t) ≡(∂)/(∂t) 𝐯 ·∇describes the rate of change as measured by somebody who moves local

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