Diferencia entre revisiones de «Partido 2»
| Línea 2: | Línea 2: | ||
\left|\begin{matrix} \vec {e_\rho} & \rho\cdot \vec {e_\theta } & \vec {e_z} \\ \frac{\partial}{\partial \rho } & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial z} \\ 0 & \rho\cdot f(\rho ) & 0 \end{matrix}\right| = \frac{1}{\rho} \cdot [\vec {e_z} \cdot (\frac{\partial}{\partial \rho } \cdot (\rho \cdot f(\rho)))] = \frac{1}{\rho} \cdot ( f(\rho) + \rho \cdot \frac{\partial f(\rho)}{\partial\rho} ) \vec {e_z} = (\frac{f(\rho )}{\rho} + \frac{\partial f(\rho)}{\partial\rho})\vec {e_z} </math> | \left|\begin{matrix} \vec {e_\rho} & \rho\cdot \vec {e_\theta } & \vec {e_z} \\ \frac{\partial}{\partial \rho } & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial z} \\ 0 & \rho\cdot f(\rho ) & 0 \end{matrix}\right| = \frac{1}{\rho} \cdot [\vec {e_z} \cdot (\frac{\partial}{\partial \rho } \cdot (\rho \cdot f(\rho)))] = \frac{1}{\rho} \cdot ( f(\rho) + \rho \cdot \frac{\partial f(\rho)}{\partial\rho} ) \vec {e_z} = (\frac{f(\rho )}{\rho} + \frac{\partial f(\rho)}{\partial\rho})\vec {e_z} </math> | ||
| − | <math>\ =(\frac{\frac{4}{3} \cdot (\rho -\frac{1}{\rho}}{\rho} + \frac{\partial(\frac{4}{3} \cdot (\rho -\frac{1}{\rho})}{\partial \rho})\vec{e_z} | + | <math>\ =(\frac{\frac{4}{3} \cdot (\rho -\frac{1}{\rho})}{\rho} + \frac{\partial(\frac{4}{3} \cdot (\rho -\frac{1}{\rho})}{\partial \rho})\vec{e_z} = [\frac{4}{3} \cdot (1 - \frac{1}{\rho^2}) + \frac{4}{3} \cdot (1 + \frac{1}{\rho^2})] \vec {e_z} = [\frac{4}{3} - \frac{4}{3\rho^2} + \frac{4}{3} + \frac{4}{3\rho^2}] \vec {e_z} = \frac{8}{3} \vec {e_z} |
Revisión actual del 00:50 7 dic 2022
[math]\ \bigtriangledown \times \vec u = \frac{1}{\rho} \cdot \left|\begin{matrix} \vec {e_\rho} & \rho\cdot \vec {e_\theta } & \vec {e_z} \\ \frac{\partial}{\partial \rho } & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial z} \\ 0 & \rho\cdot f(\rho ) & 0 \end{matrix}\right| = \frac{1}{\rho} \cdot [\vec {e_z} \cdot (\frac{\partial}{\partial \rho } \cdot (\rho \cdot f(\rho)))] = \frac{1}{\rho} \cdot ( f(\rho) + \rho \cdot \frac{\partial f(\rho)}{\partial\rho} ) \vec {e_z} = (\frac{f(\rho )}{\rho} + \frac{\partial f(\rho)}{\partial\rho})\vec {e_z} [/math]
[math]\ =(\frac{\frac{4}{3} \cdot (\rho -\frac{1}{\rho})}{\rho} + \frac{\partial(\frac{4}{3} \cdot (\rho -\frac{1}{\rho})}{\partial \rho})\vec{e_z} = [\frac{4}{3} \cdot (1 - \frac{1}{\rho^2}) + \frac{4}{3} \cdot (1 + \frac{1}{\rho^2})] \vec {e_z} = [\frac{4}{3} - \frac{4}{3\rho^2} + \frac{4}{3} + \frac{4}{3\rho^2}] \vec {e_z} = \frac{8}{3} \vec {e_z}[/math]
