Dunn Goodwin

07/30/2023 · High School

c) The divergence of \( \mathrm{v}_{\mathrm{c}} \) can be calculated as follow: \[ \begin{array}{l} \mathrm{v}_{\mathrm{c}}=\mathrm{y}^{2} \mathrm{x}+\left(2 \mathrm{xy}+\mathrm{z}^{2}\right) \mathrm{y}+2 \mathrm{yzz} \\ \Rightarrow \nabla \cdot \mathrm{v}_{\mathrm{c}}=\frac{\partial\left(\mathrm{y}^{2}\right)}{\partial \mathrm{x}}+\frac{\partial\left(2 \mathrm{xy}+\mathrm{z}^{2}\right)}{\partial \mathrm{y}}+\frac{\partial(2 \mathrm{yz})}{\partial \mathrm{z}} \\ \Rightarrow \nabla \cdot \mathrm{v}_{\mathrm{c}}=0+2 \mathrm{x}+2 \mathrm{y} \\ \Rightarrow \nabla \cdot \mathrm{v}_{\mathrm{c}}=2 \mathrm{x}+2 \mathrm{y}\end{array} \] Problem 1.16: