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Փոխվում է էջը '{{/Այս տողին խնդրում ենք ձեռք չտալ}}'-ով
Տող 1.
{{/Այս տողին խնդրում ենք ձեռք չտալ}}
 
<math>\sum_{n=1}^\infty 1/n^2 = \pi^2/6 </math>
 
<math>\frac{\partial (1-\alpha)\bar{\rho_l}}{\partial t} + \nabla \cdot \left [(1-\alpha)\bar{\rho_l} \bar{\overrightarrow{V_l}} \right ] = - \bar{\Gamma}</math>
 
<math>\frac{\partial (\alpha\bar{\rho_g})}{\partial t} + \nabla \cdot \left [\alpha\bar{\rho_g} \bar{\overrightarrow{V_g}} \right ] = \bar{\Gamma}</math>
 
<math>\rho\bar{u}_j \frac{\partial \bar{u}_i }{\partial x_j}
= \rho \bar{f}_i
+ \frac{\partial}{\partial x_j}
\left[ - \bar{p}\delta_{ij}
+ \mu \left( \frac{\partial \bar{u}_i}{\partial x_j} + \frac{\partial \bar{u}_j}{\partial x_i} \right)
- \rho \overline{u_i^\prime u_j^\prime} \right ].
</math>
 
 
:<math>\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \overrightarrow{V}) = 0</math>
 
<math>\frac{\partial \left [(1-\alpha)\bar{\rho_l} (\overline{e_l+{V_l^2/2}}) \right ]}{\partial t} + \nabla \cdot \left [(1-\alpha)\bar{\rho_l} (\overline{{e_l+{V_l^2/2}})\overrightarrow{V_l}} \right ] = - \nabla \cdot \left [(1-\alpha) \overrightarrow{\bar{q'_l}} \right ] + \nabla \cdot \left [(1-\alpha) \overline{T_l \cdot \overrightarrow{V_l}} \right ] + (1-\alpha)\bar{\rho_l}\overline{\overrightarrow{g} \cdot \overrightarrow{V_l}}-\overline{E_i}+\overline{q_{dl}} </math>
 
<math>\frac{\partial \left [\alpha\bar{\rho_g} (\overline{e_g+{V_g^2/2}}) \right ]}{\partial t} + \nabla \cdot \left [\alpha\bar{\rho_g} (\overline{{e_g+{V_g^2/2}})\overrightarrow{V_g}} \right ] = - \nabla \cdot \left [\alpha \overrightarrow{\bar{q'_g}} \right ] + \nabla \cdot \left [\alpha \overline{T_g \cdot \overrightarrow{V_g}} \right ] + \alpha\bar{\rho_g}\overline{\overrightarrow{g} \cdot \overrightarrow{V_g}}+\overline{E_i}+\overline{q_{dg}}</math>
 
<math>\frac{\partial \left [(1-\alpha)\bar{\rho_l} \overline{\overrightarrow{V_l}} \right ]}{\partial t} + \nabla \cdot (1-\alpha)\bar{\rho_l} (\overline{\overrightarrow{V_l}\overrightarrow{V_l}}) = \nabla \cdot \left [(1-\alpha) \overline{T_l} \right ] +(1-\alpha) \overline{\rho_l} \overrightarrow{g} -M_i</math>
 
<math>\frac{\partial \left [\alpha\bar{\rho_g} \overline{\overrightarrow{V_g}} \right ]}{\partial t} + \nabla \cdot \alpha\bar{\rho_g} (\overline{\overrightarrow{V_g}\overrightarrow{V_g}}) = \nabla \cdot \left [\alpha \overline{T_g} \right ] + \alpha \overline{\rho_g} \overrightarrow{g} +M_i</math>
 
<math>\frac{\partial \left [\alpha\bar{\rho_g} (\overline{e_g+{V_g^2/2}}) \right ]}{\partial t} + \nabla \cdot \left [\alpha\bar{\rho_g} (\overline{{e_g+{V_g^2/2}})\overrightarrow{V_g}} \right ] = - \nabla \cdot \left [\alpha \overrightarrow{\bar{q'_g}} \right ] + \nabla \cdot \left [\alpha \overline{T_g \cdot \overrightarrow{V_g}} \right ] + \alpha\bar{\rho_g}\overline{\overrightarrow{g} \cdot \overrightarrow{V_g}}+\overline{E_i}+\overline{q_{dg}}</math>
 
 
<math>\frac{\partial \left [(1-\alpha)\bar{\rho_l} (\overline{e_l+{V_l^2/2}}) \right ]}{\partial t} + \nabla \cdot \left [(1-\alpha)\bar{\rho_l} (\overline{{e_l+{V_l^2/2}})\overrightarrow{V_l}} \right ]</math><math> = - \nabla \cdot \left [(1-\alpha) \overrightarrow{\bar{q'_l}} \right ] + \nabla \cdot \left [(1-\alpha) \overline{T_l \cdot \overrightarrow{V_l}} \right ] + (1-\alpha)\bar{\rho_l}\overline{\overrightarrow{g} \cdot \overrightarrow{V_l}}-\overline{E_i}+\overline{q_{dl}} </math>
 
<math>E = \Gamma h'_l</math>
 
\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}
 
<math>\nabla \cdot \left [(1-\alpha)\bar{\rho_l} (\overline{{e_l+{V_l^2/2}})\overrightarrow{V_l}} \right ] </math>
 
 
<math>\nabla \cdot \left [(1-\alpha) \overline{T_l \cdot \overrightarrow{V_l}} \right ] = - \nabla \cdot \left [(1-\alpha) \overline{P} \overline{\overrightarrow{V_l}} \right ] + W_l =</math>
 
<math>\frac{\partial \left [(1-\alpha)\bar{\rho_l} (\overline{e_l+{V_l^2/2}}) \right ]}{\partial t} + \nabla \cdot \left [(1-\alpha)\bar{\rho_l} (\overline{{e_l+{V_l^2/2}})\overrightarrow{V_l}} \right ] </math><math>= - \nabla \cdot \left [(1-\alpha) \overrightarrow{\bar{q'_l}} \right ] - \nabla \cdot \left [(1-\alpha) \overline{P} \overline{\overrightarrow{V_l}} \right ] + W_l + (1-\alpha)\bar{\rho_l}\overline{\overrightarrow{g} \cdot \overrightarrow{V_l}}-\Gamma h'_l+\overline{q_{dl}} </math>
 
 
<math>\frac{\partial \left [(1-\alpha)\bar{\rho_l} (\overline{e_l+{V_l^2/2}}) \right ]}{\partial t} + \nabla \cdot \left [(1-\alpha)\bar{\rho_l} (\overline{{e_l+\frac{P}{\rho_l}+{V_l^2/2}})\overrightarrow{V_l}} \right ] = - \nabla \cdot \left [(1-\alpha) \overrightarrow{\bar{q'_l}} \right ] + W_l + (1-\alpha)\bar{\rho_l}\overline{\overrightarrow{g} \cdot \overrightarrow{V_l}}-\Gamma h'_l+\overline{q_{dl}} </math>
 
 
<math>\frac{\partial \left [\overline{(1-\alpha)\bar{\rho_l} (e_l+{V_l^2/2})} \right ]}{\partial t} +\overline{\nabla \cdot \left [(1-\alpha)\bar{\rho_l} ({e_l+\frac{P}{\rho_l}+{V_l^2/2}})\overrightarrow{V_l} \right ]} = - \overline{\nabla \cdot \left [(1-\alpha) \overrightarrow{q'_l} \right ]} + \overline{(1-\alpha)\bar{\rho_l}\overrightarrow{g} \cdot \overrightarrow{V_l}-\Gamma h'_l+ W_l} +\overline{q_{dl}} </math>
 
 
<math>\frac{\partial \left [\overline{\alpha\bar{\rho_g} (e_g+{V_g^2/2})} \right ]}{\partial t} +\overline{\nabla \cdot \left [(1-\alpha)\bar{\rho_g} ({e_g+\frac{P}{\rho_g}+{V_g^2/2}})\overrightarrow{V_g} \right ]} = - \overline{\nabla \cdot \left [\alpha \overrightarrow{q'_g} \right ]} + \overline{\alpha\bar{\rho_g}\overrightarrow{g} \cdot \overrightarrow{V_g}+\Gamma h'_v+ W_g} +\overline{q_{dg}} </math>
 
 
<math>= P+R</math>
 
<math>\frac{\partial \left [(1-\alpha)\bar{\rho_l} \overline{\overrightarrow{V_l}} \right ]}{\partial t} + \nabla \cdot (1-\alpha)\bar{\rho_l} (\overline{\overrightarrow{V_l}\overrightarrow{V_l}}) = \nabla \cdot \left [(1-\alpha) \overline{R_l} \right ] +(1-\alpha) \overline{\rho_l} \overrightarrow{g} -M_i</math>
 
<math>\frac{\partial \overline{\left [(1-\alpha)\rho_l\overrightarrow{V_l} \right ]}}{\partial t} + \overline{\nabla \cdot (1-\alpha)\rho_l (\overrightarrow{V_l}\overrightarrow{V_l})} = \overline{\nabla \cdot \left [(1-\alpha) R_l \right ]} + \overline{(1-\alpha) \rho_l \overrightarrow{g} -M_i}</math>
 
<math>\frac{\partial \overline{\left [\alpha\rho_g\overrightarrow{V_g} \right ]}}{\partial t} + \overline{\nabla \cdot \alpha\bar{\rho_g} (\overrightarrow{V_g}\overrightarrow{V_g})} = \overline{\nabla \cdot \left [\alpha R_g \right ]} + \overline{\alpha \rho_g \overrightarrow{g} +M_i}</math>
 
<math>\frac{\partial \overline{\left [(1-\alpha)\rho_l\right ]}}{\partial t} + \overline{\nabla \cdot \left [(1-\alpha)\rho_l \overrightarrow{V_l} \right ]} = - \bar{\Gamma}</math>
 
<math>\frac{\partial \overline{\left (\alpha\rho_g\right )}}{\partial t} + \overline{\nabla \cdot \left [\alpha\rho_g \overrightarrow{V_g} \right ]} = \bar{\Gamma}</math>
 
<math>\frac{dm_H}{dt} = g_H - \frac{m_H}{m_H+m_S}G</math>
 
<math>\frac{dm_S}{dt} = g_S - \frac{m_S}{m_H+m_S}G</math>
 
<math>G</math>
 
<math>m_S</math>
 
<math>G = g_S + g_H</math>
 
<math>C_H = \frac{m_H}{m_H+m_S}</math>
 
<math>C_S = \frac{m_S}{m_H+m_S}</math>
 
<math>M\frac{dC_H}{dt} = g_H - C_HG</math>
 
<math>M\frac{dC_S}{dt} = g_S - C_SG</math>
 
<math>\frac{dm_S}{dt} = g_S - \frac{m_S}{m_H+m_S}G</math>
 
<math>C_S = \frac{g_S}{G} - C_{S0} \cdot e^{-\frac{G}{M}t}</math>
 
 
<math>C_S = \frac{g_S}{G}</math>
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