基本概念
$$ \frac{1}{2}\rho v^2 + \rho gh + p = const $$
证明过程
做功能量、动能变化、势能变化分别为：
$$ \begin{aligned} &\Delta E_w = p_1A_1v_1\Delta t - p_2A_2v_2\Delta t\ ~\ &\Delta E_k = \frac{1}{2}\rho A_1v_1\Delta tv_1^2 - \frac{1}{2}\rho A_2v_2\Delta tv_2^2\ ~\ &\Delta E_g = \rho A_1v_1\Delta tgh_1 - \rho A_2v_2\Delta tgh_2 \end{aligned} $$
能量守恒：
$$ \Delta E_w + \Delta E_k + \Delta E_g = 0 $$
假设流体不可压缩：
$$ A_1v_1 = A_2v_2 = const $$
带入可得：
$$ \frac{1}{2}\rho v_1^2 + \rho gh_1 + p_1 = \frac{1}{2}\rho v_2^2 + \rho gh_2 + p_2 $$