The purpose of this and next problem is to calculate and compare pressure drops under various

situations to get a feel for the magnitudes of pressure drops due to viscous dissipation, constrictions,

and height changes. Comparing problem $1$ and $2$ will give you a feel for differences between gases

and liquids. Oil with $300cp$ viscosity and $0\mathrm{.}85\frac{g}{c}{m}^3$ density is flowing in a pipe that is $4ft$ in

diameter at a rate of $10\frac{m^3}{m}in.$ These parameters are those typical of the Alaskan oil pipeline.

$($a$)$ What does Bernouilli's equation predict for pressure drop for a completely horizontal $1$ mile

section of this pipe?

$($b$)$ What does the Hagen$-$Poiseuille equation predict for pressure drop for a completely horizontal

$1$ mile section of this pipe? Also calculate Re to justify use of Hagen$-$Poiseuille equation. When

is this equation valid?

$($c$)$ Why is there a difference in the answers for a and b$.$ Which is correct?

At some point along this pipe there is a sudden change $($a constriction$)$ in the diameter of the pipe

from $4ft$ to $2ft$ without changing the height of the pipes centerline.

$($d$)$ What does Bernouilli's equation predict for pressure drop between a point $100ft$ before this

pipe and $100ft$ after this pipe?

$($e$)$ What does Hagen$-$Poiseuille equation predict for pressure drop between a point $100ft$ before

this pipe and $100ft$ after this pipe?

$($f$)$ Why is there a difference in the answers for $d$ and e$?$ Which is correct?

At some point along this $4ft$ diameter pipe there is a $100ft$ high hill.

$($g$)$ What does Bernouilli's equation predict for pressure drop between the bottom and top of this

hill?

$($h$)$ What does Hagen$-$Poiseuille equation predict for pressure drop between the bottom and top

of this hill?

$($i$)$ Is there a difference between the answers in $($g$)$ and $($h$)?$ Why or why not?

$($j$)$ What did you learn by doing the above problems? Make a list of things you learned.