Վիքիգրքեր:Ավազարկղ

Վիքիգրքեր-ից
Ավազարկղ
Bucket in the sand.svg
Բարի գալո՛ւստ հայերեն Վիքիգրքեր

Այս ավազարկղից կարող եք օգտվել Վիքիգրքերի խմբագրման ոճին և գործիքներին ծանոթանալու համար։ Խնդրեմ ազատ զգացեք այստեղ խմբագրումներ անել, առանց վախենալու, որ որևէ էջ կփչացնեք։ Այս էջի բովանդակությունը հերթականաբար ջնջվելու/փոփոխվելու է։


\sum_{n=1}^\infty 1/n^2 = \pi^2/6

\frac{\partial (1-\alpha)\bar{\rho_l}}{\partial t} + \nabla \cdot \left [(1-\alpha)\bar{\rho_l} \bar{\overrightarrow{V_l}} \right ] = - \bar{\Gamma}

\frac{\partial (\alpha\bar{\rho_g})}{\partial t} + \nabla \cdot \left [\alpha\bar{\rho_g} \bar{\overrightarrow{V_g}} \right ] = \bar{\Gamma}

\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 ].


\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \overrightarrow{V}) = 0

\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}}

\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}}

\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

\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

\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}}


\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}}

E = \Gamma h'_l

\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}

\nabla \cdot \left [(1-\alpha)\bar{\rho_l} (\overline{{e_l+{V_l^2/2}})\overrightarrow{V_l}} \right ]


\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 =

\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{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}}


\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}}


\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}}


\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}}


= P+R

\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

\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}

\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}

\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}

\frac{\partial \overline{\left (\alpha\rho_g\right )}}{\partial t} + \overline{\nabla \cdot \left [\alpha\rho_g \overrightarrow{V_g} \right ]} = \bar{\Gamma}

\frac{dm_H}{dt} = g_H - \frac{m_H}{m_H+m_S}G

\frac{dm_S}{dt} = g_S - \frac{m_S}{m_H+m_S}G

G

m_S

G = g_S + g_H

C_H = \frac{m_H}{m_H+m_S}

C_S = \frac{m_S}{m_H+m_S}

M\frac{dC_H}{dt} = g_H - C_HG

M\frac{dC_S}{dt} = g_S - C_SG

\frac{dm_S}{dt} = g_S - \frac{m_S}{m_H+m_S}G

C_S = \frac{g_S}{G} - C_{S0} \cdot e^{-\frac{G}{M}t}


C_S = \frac{g_S}{G}