BA Beat Teuber: Difference between revisions
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(Created page with "== Herleitung der Kraft in einen Zylinder == \[\vec{F} = \int\limits_\text{O} \sigma \mathrm{d} \vec{A} \] Da \(\vec{A} = A \vec{e}_\mathrm{\rho}\), gilt \[\vec{F} = \int\limits_\text{O} (\sigma_\mathrm{\rho\rho} \vec{e}_\text{r} + \sigma_\mathrm{\varphi\rho} \vec{e}_\mathrm{\rho} + \sigma_{\text{z}\mathrm{\rho}} \vec{e}_\text{z}) \mathrm{d} A\] mit \[\sigma=-p\mathbb{1} + \mu \left( \vec{\nabla} \vec{u} + \left(\vec{\nabla} \vec{u}\right)^\mathrm{T} - \frac{2}{3} \...") |
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Da \(\vec{A} = A \vec{e}_\mathrm{\rho}\), gilt | Da \(\vec{A} = A \vec{e}_\mathrm{\rho}\), gilt | ||
\[\vec{F} = \int\limits_\text{O} (\sigma_\mathrm{\rho\rho} \vec{e}_\ | \[\vec{F} = \int\limits_\text{O} (\sigma_\mathrm{\rho\rho} \vec{e}_\mathrm{\rho} + \sigma_\mathrm{\varphi\rho} \vec{e}_\mathrm{\varphi} + \sigma_{\text{z}\mathrm{\rho}} \vec{e}_\text{z}) \mathrm{d} A\] | ||
mit | mit | ||
\[\sigma=-p\mathbb{1} + \mu \left( \vec{\nabla} \vec{u} + \left(\vec{\nabla} \vec{u}\right)^\mathrm{T} - \frac{2}{3} \vec{\nabla} \cdot \vec{u} \mathbb{1} \right)\] | \[\sigma=-p\mathbb{1} + \mu \left( \vec{\nabla} \vec{u} + \left(\vec{\nabla} \vec{u}\right)^\mathrm{T} - \frac{2}{3} \vec{\nabla} \cdot \vec{u} \mathbb{1} \right)\] | ||
Revision as of 15:27, 30 June 2025
Herleitung der Kraft in einen Zylinder
\[\vec{F} = \int\limits_\text{O} \sigma \mathrm{d} \vec{A} \]
Da \(\vec{A} = A \vec{e}_\mathrm{\rho}\), gilt
\[\vec{F} = \int\limits_\text{O} (\sigma_\mathrm{\rho\rho} \vec{e}_\mathrm{\rho} + \sigma_\mathrm{\varphi\rho} \vec{e}_\mathrm{\varphi} + \sigma_{\text{z}\mathrm{\rho}} \vec{e}_\text{z}) \mathrm{d} A\]
mit
\[\sigma=-p\mathbb{1} + \mu \left( \vec{\nabla} \vec{u} + \left(\vec{\nabla} \vec{u}\right)^\mathrm{T} - \frac{2}{3} \vec{\nabla} \cdot \vec{u} \mathbb{1} \right)\]