CH$-8$ Air flows through a smooth tube, $2\mathrm{.}5$ cm diameter and $10$ m long, at $37C.$ If the pressure drop through the tube is $10000$ Pa $,$ estimate

$($a$)$ the air velocity through the tube and the friction factor

$($b$)$ the heat transfer coefficient using Colburn Analogy $[j_H=(St)(Pr{)}^{0\mathrm{.}67}],$ where St is the Stanton Number and Pr is the Prandtl Number.

Gas constant, $R=82\mathrm{.}06c{m}^3$ atm$/$mol K$.$ Darcy friction factor, $f=\frac{0\mathrm{.}184}{R}{e}^{0\mathrm{.}2}.$

Other relevant properties of air under the given conditions : viscosity $=1\mathrm{.}8{10}^{-5}k\frac{g}{m}s,$ density $=1\mathrm{.}134k\frac{g}{m^3},$ specific heat capacity, $Cp=1\mathrm{.}046k\frac{J}{k}{g}^{0}C,$ thermal conductivity $=0\mathrm{.}028\frac{W}{m^0}C.$