Capture_5：Mass And Energy Analyse of Control Volumes 体积控制系统质量、能量分析
Capture_5: Mass And Energy Analyse of Control Volumes 体积控制系统质量、能量分析
Summary
Conservation of mass principal
\[ \begin{cases}m_{\text {in }}-m_{\text {out }}=\Delta m_{system} & \\ \dot{m}_{\text {in }}-\dot{m}_{\text {out }}=d m_{system} / d t \end{cases} \]
- a cross section: 横截面
mass flow rate 质量流速度
amount of mass flowing through a cross section par unit time 单位时间穿过某横截面的质量：
$$ =v A
$$
其中：
- A：area normal
volume flow rate 体积流速度 ：
\[ \dot{U}=v A=\dot{m} / p \]
flow work 功流量 ：
\[ w_{\text {flow }}=P \cdot v \]
Total Energy of a flowing fluid 流体总能量:
$$ =h+k e+p e=h++g z
$$
Hate of energy trasport 能量转移速率：\(\dot{m} \theta\)
\[ when\ k_{e}=p_e=0：\left\{\begin{array}{l}E_{\text {mass }}=m h \\ \dot{E} _\text { mass }=\dot{m} h .\end{array}\right. \]
※Steady flow 定常流动
Steady flow 定常流动
\(\left\{\begin{array}{l} \Sigma_{\text {in }} \dot{m}=\Sigma_{\text {out }} \dot{m} \\ \dot{Q}-\dot{w}=\Sigma_{\text {out}} \dot{m}\left(h+\frac{v^{2}}{2}+g z\right)-\Sigma_{\text {in }} \dot{m}\left(h+\frac{v^{2}}{2}+g z\right) \end{array}\right.\)
Single Steady flow 单定常流动
\(\left\{\begin{array}{l} m_{1}=m_{2} \rightarrow \frac{1}{\nu_{1}} V_{1} A_{1}=\frac{1}{\nu_{2}} \cdot V_{2} A_{2} \\ \left.\dot{Q}-\dot{W}=\dot{m}\left[h_{2}-h_{1}+\frac{V_{2}^{2}-V_{1}^{2}}{2}+g ( z_{2}-z_{1}\right)\right] \end{array}\right.\)
unsteady flow 非定常流动\(\Rightarrow\)uniform-flow-process 均匀流动过程
\[ \begin{align}\left\{\begin{aligned}& m_{in}-m_{out} = \Delta m_{system} \\ &Q-W = \sum_{out}mh_{out}-\sum_{in}h_{in}+(m_2u_2-m_1u_1)\end{aligned}\right.\end{align} \]
