Question $7$: Pipe Flow $($find P$3)$

Water flows steadily within a pipe at constant density $=999\mathrm{.}1k\frac{g}{m^3}.$ Three locations are marked on the pipe. Location $1$ is at the beginning of the straight pipe segment, location $2$ is at the end of the straight pipe segment or the beginning of the elbow, and location $3$ is at the end of the elbow. The straight pipe segment has:

inner diameter: $D=0\mathrm{.}07m$

length: $L=0\mathrm{.}91m$

friction factor: $f=0\mathrm{.}08.$

The elbow inside the CV has:

inner diameter: $D=0\mathrm{.}07m($same as straight pipe segment$)$

height: $H=0\mathrm{.}23m$

Velocities are approximately uniform over $A_1,A_2,$ and $A_3.$ If the flow is $Q=0\mathrm{.}015\frac{m^3}{s},$ and $P_2=17$kPa, calculate $P_3.$ Hints: use the given values for $f$ and $K_L,$ even though you know other ways to estimate these values.