An intravenous $($IV$)$ system is supplying saline solution to a patient at the rate of $0\mathrm{.}1982$cm$3/$s$0\mathrm{.}1982$cm$3/$s through a needle of radius $0\mathrm{.}16$mm$0\mathrm{.}16$mm and length $2\mathrm{.}4$cm$2\mathrm{.}4$cm$.$ The gauge pressure of the blood in the patient's vein is $8\mathrm{.}00$mm Hg$8\mathrm{.}00$mm Hg$.($Assume the density and viscosity of saline solution is the same as seawater and the temperature is $20$C$20$C$).$

hilarytaylor@ufl.edu$1$F$76-$CC$-$F$6-40-9895-54959$

$-$ Part $($a$)$

Calculate the gauge pressure of the saline solution at the patient's vein if the IV bag is hung at a height $1\mathrm{.}95$m$1\mathrm{.}95$m above the injection site. The IV bag is at atmospheric pressure, and you may assume that there is sufficient saline solution in the bag to treat the solution in the IV line as a static column of fluid. Give your answer in pascals.

PP $=1\mathrm{.}9181041\mathrm{.}918104$PaPa$$Correct$!$

$$ Part $($b$)$

Calculate the new flow rate, in cubic centimeters per second, if the height of the saline solution is decreased to $1\mathrm{.}5$m$1\mathrm{.}5$m$.$ The viscosity of seawater is $0\mathrm{.}001002$Pa$$s$0\mathrm{.}001002$Pa$$s$.$

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