$13.$ Trickle Bed Reactors: A trickle bed reactor operates with a liquid superficial velocity of $0\mathrm{.}01$ m$/$s and a gas superficial velocity of $0\mathrm{.}5$ m$/$s$.$ Calculate the pressure drop across a $1$ m section of the bed.

$14.$ Flow Regime Identification: Given a pipe with an internal diameter of $50$ mm carrying a gas$-$liquid flow at superficial velocities of $1$ m$/$s for gas and $0\mathrm{.}1$ m$/$s for liquid, identify the flow regime using the Baker chart.

$15.$ Pressure Drop in Three$-$Phase Flow: For a $10$ m long horizontal pipe with a diameter of $200$ mm carrying a three$-$phase flow $($gas$,$ liquid, solid$)$ with phase velocities of $2$ m$/$s$,0\mathrm{.}5$ m$/$s$,$ and $0\mathrm{.}05$ m$/$s respectively, estimate the total pressure drop.

$16.$ Volume Fraction Estimation in Packed Beds: With a packed bed containing spheres of diameter $10$ mm at a bed porosity of $0\mathrm{.}4,$ calculate the volume fraction of the solid phase.