In a laboratory experiment, air $)=1\mathrm{.}2\frac{kg}{m^3},=(0\mathrm{.}000015\frac{kg}{m}.s$ flows from a very large air tank through a $2cm$ diameter smooth pipe open to atmosphere as shown. The flow is metered

by a long$-$radius nozzle of $1cm$ diameter, using oil $)=(0\mathrm{.}827.$ The pipe is $8m$ long. Following measurements were taken at different flow rates.

$\backslash$table$[[$Tank Pressure $P_{\text{g}\text{a}\text{g}\text{e}}(Pa),60,320,1200,2050,2470,3500,4900],[$Manometer Reading $h(mm),6,38,160,295,380,575,820],[$Friction factor $f,,,,,,,],[$Volume Flow rate $\frac{m^3}{h}r($theory$),,,,,,,],[$Volume Flow rate $\frac{m^3}{h}r($measured$),,,,,,,]]$

$($a$)$ For each data point, compute the volume flow rate $(\frac{m^3}{h}r)$ using the energy equation and pipe flow analysis. Assume a smooth pipe $($i$.$e roughness is negligible, but friction losses are present$).$ Consider major and minor losses. Assume minor loss coefficients for entrance $)=(0\mathrm{.}5$ and nozzle $)=(0\mathrm{.}7.$ Enter friction factor $f$ and volume flow rate values $($theory$)$ in the above table. Either use Moody's chart $($or the Colebrook relation, this might be better as several data points are given$).$ Clearly tabulate your iterations $($as done in class$)$ and provide all details. Clearly show all logical steps.

$($b$)$ Compute the volume flow rate $(\frac{m^3}{h}r)$ using the measured manometer reading across the nozzle $($you will have to first relate the manometer reading and area change across nozzle to the velocity through the nozzle throat and then obtain the flow rate$).$ Enter this value in the above table as well.

$($c$)$ Plot $($using Matlab or other software$),$ flow rate versus the tank gage pressure. Use solid line for the flow rate obtained from the pipe flow analysis and square symbols for the flow rate obtained from the manometer reading. Both should be plotted on the same figure with proper legend given. Show all steps and attach your program or procedure used to solve this part.

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