Figure $4$: Pipe with contraction.

The pipe system shown in Figure $4$ first rises a height $h$ then contracts from a diameter $D_1=5cm$ to $D_2=3cm.$ If

the pipe is moving an inviscid, dense slurry with a density $=9600k\frac{g}{m^3},$ and the pressure gauges read the following

in gauge pressure: $P_1=90$kPa,$P_2=55$kPa, and $P_3=20$kPa find the following:

$($a$)$ Find the height difference, $h,$ that the pipe system rises.

$($b$)$ Determine the flow rate, $Q,$ through the system.