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

$$\{\begin{array}{ll}{m}_{\text{in }}-m_{\text{out }}=\mathrm{\Delta }{m}_{system}& \\ {\dot{m}}_{\text{in }}-{\dot{m}}_{\text{out }}=d{m}_{system}/dt\end{array}$$

• 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 ：

$$\dot{U}=vA=\dot{m}/p$$

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：$\dot{m}\theta$

$$when{k}_e=p_e=0：\{\begin{array}{l}{E}_{\text{mass }}=mh\\ {\dot{E}}_{\text{ mass }}=\dot{m}h.\end{array}$$

※Steady flow 定常流动

Steady flow 定常流动

$\{\begin{array}{l}{\mathrm{\Sigma }}_{\text{in }}\dot{m}={\mathrm{\Sigma }}_{\text{out }}\dot{m}\\ \dot{Q}-\dot{w}={\mathrm{\Sigma }}_{\text{out}}\dot{m}(h+\frac{v^2}{2}+gz)-{\mathrm{\Sigma }}_{\text{in }}\dot{m}(h+\frac{v^2}{2}+gz)\end{array}$

Single Steady flow 单定常流动

$\{\begin{array}{l}{m}_1=m_2\to \frac{1}{{\nu }_1}{V}_1{A}_1=\frac{1}{{\nu }_2}\cdot V_2{A}_2\\ \dot{Q}-\dot{W}=\dot{m}[h_2-h_1+\frac{V_2^2-V_1^2}{2}+g(z_2-z_1)]\end{array}$

unsteady flow 非定常流动$\Rightarrow$uniform-flow-process 均匀流动过程

$$\begin{array}{}\text{(1)}& \{\begin{array}{rl}& m_{in}-m_{out}=\mathrm{\Delta }{m}_{system}\\ & Q-W=\sum _{out}m{h}_{out}-\sum _{in}{h}_{in}+(m_2{u}_2-m_1{u}_1)\end{array}\end{array}$$