$($Please follow the steps, show work and answer the question$)$

Must follow the steps of the Problem$-$Solving Method $($PSM$)$ shown:

a$)$ Write down the problem

b$)$ Define the problem: Define one or more criteria $($measures$)$ for answering the

question, if one is not explicitly given in the problem statement

c$)$ Explore the problem: Generate appropriate questions related to the "measures"

defined in Step $1,$ identify possible approaches $($models$)$ for solving the problem, and make

reasonable assumptions.

d$)$ Plan the solution: Select appropriate values of known and assumed quantities in the

equations and carry out calculations correctly. Produce sketches, figures, and drawings as

necessary.

e$)$ Implement the solution: Substitute appropriate values of know and assumed

quantities in the equations and carry out calculations correctly. Produce sketches, figures, and

drawings as necessary.

f$)$ Evaluate the results: Discuss whether answers make sense and evaluate the

appropriateness of models used and assumptions made. Reflect on your personal strengths

and weaknesses in applying the problem$-$solving methodology.

Write down all the steps,

Explain all your assumptions.

Provide clear sketches,

Write units in your 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 $.$