The design data for a pipe at the outlet of an oil$-$field steam generator are as follows:

$,$ Pipe size and schedule: $3$ NPS$,$ Sch $160,$ carbon steel, ID $=66\mathrm{.}6mm$

Total steam mass flow: $27,800k\frac{g}{h}$

$,$ Steam quality: $70\%$

$,$ Steam Pressure $=13,700$kPag$=2000$ psia

Barometric pressure $=90$kPa

Density: liquid $=624k\frac{g}{m}3,$ vapour $=85\mathrm{.}2k\frac{g}{m}3$

Viscosity: liquid $=0\mathrm{.}091$mPa.$s,$ vapour $=0\mathrm{.}025$mPa.$s($Note: $1$mPa.$s=1cP)$

$,$ Pipe straight length $=10m$

$,$ Pipe surface roughness factor $=0\mathrm{.}046mm$

Calculate the pressure drop of the two$-$phase flow of $70\%$ quality steam, in the above pipe,

using the homogeneous model $2-$phase frictional multiplier $(\frac{O}{{?}_{f_o}}2)$ method provided in this

examination booklet. Add $20\%$ design margin.

Plot the f factor on the friction factors chart provided.