1 1 vote Let $\rho(x, y, z, t)$ and $u(x, y, z, t)$ represent density and velocity, respectively, at a point $(x, y, z)$ and time $t$. Assume $\frac{\partial \rho}{\partial t}$ is continuous. Let $V$ be an arbitrary volume in space enclosed by the closed surface $S$ and $\hat{n}$ be the outward unit normal of $S$ Which of the following equations is/are equivalent to $\frac{\partial \rho}{\partial t}+\nabla \cdot(\rho u)=0$? $\int_{V} \frac{\partial \rho}{\partial t} d v=-\oint_{S} \rho u \cdot \hat{n} d s$ $\int_{V} \frac{\partial \rho}{\partial t} d v=\oint_{S} \rho u \cdot \hat{n} d s$ $\int_{V} \frac{\partial \rho}{\partial t} d v=-\int_{V} \nabla \cdot(\rho u) d v$ $\int_{V} \frac{\partial \rho}{\partial t} d v=\int_{V} \nabla \cdot(\rho u) d v$ Vector Analysis gateece-2024 continuity-and-differentiability vector-analysis calculus + – admin 1.7k views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
