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GATE EC 2024 Set 1 — Question 25

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MSQ+1 / -0MediumGauss, Stokes & Green's TheoremsVector CalculusEngineering Mathematics

Engineering Mathematics → Vector Calculus → Gauss, Stokes & Green's Theorems

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Question

Let ρ(x,y,z,t)\rho(x, y, z, t) and u(x,y,z,t)u(x,y,z,t) represent density and velocity, respectively, at a point (x,y,z)(x, y, z) and time tt. Assume ∂ρ∂t\frac{\partial \rho}{\partial t} is continuous. Let VV be an arbitrary volume in space enclosed by the closed surface SS and n^\hat{n} be the outward unit normal of SS. Which of the following equations is/are equivalent to ∂ρ∂t+∇⋅(ρu)=0\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho u) = 0?
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