Finish

$$\hbox{\epsffile{figures/total.ps}}$$

$$0 = p_1 - p_A + p_A - p_D + p_D - p_2$$

Individual pressure differences:

$$\frac{p_1}{\rho} + gh_1 = \frac{p_A}{\rho} + {\textstyle\frac{1}{2}} v^2$$

$$\frac{p_A}{\rho} + {\textstyle\frac{1}{2}} v^2 = \frac{p_D}... ...style\frac{1}{2}} v^2 + f \frac Lh {\textstyle\frac{1}{2}} v^2$$

$$\frac{p_D}{\rho} + \alpha {\textstyle\frac{1}{2}} v^2 = \frac{p_2}{\rho} +g h_2 + K_D {\textstyle\frac{1}{2}} v^2 + g h_2$$

Total:

$$g h_1 - g h_2 = K_e {\textstyle\frac{1}{2}} v^2 + f \frac{... ... {\textstyle\frac{1}{2}} v^2 + K_D {\textstyle\frac{1}{2}} v^2$$

where $v$ is the average velocity in the duct.