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：

$$\dot{m}=\rho \cdot v \cdot A$$

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:

$$\theta=h+k e+p e=h+\frac{v^{2}}{2}+g z$$

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

$$\begin{align}\left\{\begin{aligned}& m_{in}-m_{out} = \Delta m_{system} \\ &Q-W = \sum_{out}mh_{out}-\sum_{in}h_{in}+(m_2u_2-m_1u_1)\end{aligned}\right.\end{align}$$