$($Please show work and explain steps. Circle$/$box final answers$)$

Problem $($Choice A$).$

An Astronaut who is on a mission in a very unfamiliar and hazardous area in the Moon environment

is wearing an emergency protective spacesuit. The Astronaut is supplied with oxygen at an average

rate of $0\mathrm{.}06$kg$//$s through an artificial "umbilical cord" which is conceptualized as a duct connected

to the spacesuit. The duct has a length of L$(796$cm L cm$).$ The pressure p and temperature

T of the oxygen at the inlet to the duct are maintained constant to $250+-0\mathrm{.}5$kPa and $10^($@$)$C$,$

respectively, and the pressure at the outlet end of the channel is $50+-0\mathrm{.}1$kPa. As a newly hired

member of the emergency design team, your responsibility is to help ensure the astronaut's safety

and the successful completion of the mission. You are tasked with determining the average effective

diameter of the duct, given that the only available duct material has an effective relative wall

roughness epsi of $0\mathrm{.}005$ mm $.$