What is the maximum flow rate through the pipe shown in Fig. P$7\mathrm{.}129$ if the elevation difference of the reservoir surfaces is $80m?$

Solution:

Use an average value of $e,$ so $e=mm$;

Relative roughness $=$

Assuming a relative large Re so we can use the horizontal portion of the line on Moody chart, thus $f$ can be found nearly $f=$

There are in total $$ hydraulic fittings, total energy loss is

$h_f=\frac{v^2}{2g}$;

$h_m=\frac{v^2}{2g}$;

Thus, for the elevation difference given, velocity of the flow in the pipe is $v=\frac{m}{s}$

Hence, the flow rate is $Q=\frac{m^3}{s}$

Check the $Re={10}^6.$ This is sufficiently large.