Question $3$: Aspirator $($revised$)$

Air flows steadily at constant density ${}_a=1\mathrm{.}23k\frac{g}{m^3}$ in this aspirator nozzle made from round pipes $($see image$).$ The aspirator

design attempts to produce a vacuum condition at $P_3.$ The air flows horizontally from location $1$ to $2$ and then continues

horizontally. You can use Pascal's Principle between locations $2$ and $3.$ The heights are as follows: radius $r_1=0\mathrm{.}24m,$ radius $r_2=0\mathrm{.}03$

m $,$ and height $H=0\mathrm{.}5m.$ Given the flowrate of air is $Q=38$ liters $\frac{?}{s},$ the pressure $P_1=16Pa,$ and head loss $(h_{L12})=0\mathrm{.}1m,$ calculate

the pressure at location $3.$

humber $($rtol $=0\mathrm{.}02,$ atol $=1e-08)$