Mecânica dos fluidos/Fluxo laminar do líquido Newtoniano: diferenças entre revisões
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Linha 15:
<center><math>- \; \frac{\partial p}{\partial x} \;+\; \mu_0 \left( \frac{\partial ^2 v_x}{\partial x ^2} \;+\; \frac{\partial ^2 v_x}{\partial y ^2} \;+\; \frac{\partial ^2 v_x}{\partial z ^2} \right) \;-\; \rho_0 g_x \;=\; \rho_0 \left( v_x \frac{\partial v_x}{\partial x} \;+\; v_y \frac{\partial v_x}{\partial y} \;+\; v_z \frac{\partial v_x}{\partial z} \;+\; \frac{\partial v_x}{\partial t} \right)</math></center>
<center><math>- \; 0 \;+\; \mu_0 \left( 0 \;+\; 0 \;+\; \frac{\partial ^2 v_x}{\partial z ^2} \right) \;-\; \rho_0 g \sin \theta \;=\; \rho_0 \left( 0 \;+\; 0 \;+\; 0 \;+\; 0 \right) \Rightarrow \;\;\; \mu_0 \frac{\partial ^2 v_x}{\partial z ^2} \;=\; \rho_0 g \sin \theta</math></center>
Similarmente, para o eixo Y
<center><math>- \; \frac{\partial p}{\partial y} \;+\; \mu_0 \left( \frac{\partial ^2 v_y}{\partial x ^2} \;+\; \frac{\partial ^2 v_y}{\partial y ^2} \;+\; \frac{\partial ^2 v_y}{\partial z ^2} \right) \;=\; \rho_0 \left( v_y \frac{\partial v_x}{\partial x} \;+\; v_y \frac{\partial v_y}{\partial y} \;+\; v_z \frac{\partial v_y}{\partial z} \;+\; \frac{\partial v_x}{\partial t} \right)</math></center>
<center><math>0 \;+\; \mu_0 \left( 0 \;+\; 0 \;+\; 0 \right) \;=\; \rho_0 \left( 0 \;+\; 0 \;+\; 0 \;+\; 0 \right)</math></center>
E, para o eixo Z
<center><math>\;-\; \; \frac{\partial p}{\partial z} \;+\; \mu_0 \left( \frac{\partial ^2 v_z}{\partial x ^2} \;+\; \frac{\partial ^2 v_z}{\partial y ^2} \;+\; \frac{\partial ^2 v_z}{\partial z ^2} \right) \;-\; \rho_0 g_z \;=\; \rho_0 \left( v_x \frac{\partial v_z}{\partial x} \;+\; v_y \frac{\partial v_z}{\partial y} \;+\; v_z \frac{\partial v_z}{\partial z} \;+\; \frac{\partial v_z}{\partial t} \right)</math></center>
<center><math>\;-\; \; \frac{\partial p}{\partial z} \;+\; \mu_0 \left( 0 \;+\; 0 \;+\; 0 \right) \;-\; \rho_0 g \cos \theta \;=\; \rho_0 \left( 0 \;+\; 0 \;+\; 0 \;+\; 0 \right) \Rightarrow \;\;\; \frac{\partial p}{\partial z} \;=\; - \; \rho_0 g \cos \theta</math></center>
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