$7$B$.12$ Criterion for vapor$-$free flow in a pipeline. To ensure that a pipeline is completely liquid$-$

filled, it is necessary that $p>p_{\text{v}\text{a}\text{p}}$ at every point. Apply this criterion to the system in Fig. $7\mathrm{.}5-1,$

by using mechanical energy balances over appropriate portions of the system

$.$Fig. $7\mathrm{.}5-1.$ Pipeline flow

with friction losses be$-$

cause of fittings. Planes

$1$ and $2$ are just under

the surface of the liquid.