Problem $4$:

The following data are given in a location in a pipe where the average pressure and temperature are $1400$ psia and $120F$ :

$v_{SL}=3\mathrm{.}5f\frac{t}{sec}$

${}_L=7cP$

${}_L=80l\frac{b}{f}{t}^3$

$d=4\mathrm{.}5in$

${}_L=6\mathrm{.}7$ dynes $\frac{?}{cm}$

$v_{Sg}=14\mathrm{.}0f\frac{t}{sec}$

${}_g=0\mathrm{.}02cP$

${}_g=5\mathrm{.}5l\frac{b}{f}{t}^3$

$=0\mathrm{.}00006ft$

Calculate the total pressure gradient using Beggs and Brill correlation for upward vertical flow.