For the one$-$dimensional fluid flow through the stepped porous medium shown in figure, determine the pressure at the junction of each area. Also determine the velocities in each element. Let Kxx $=1$in$./$s$.$Consider water at $20$Celsius$.$ The pressure at point $1,$ p$1,$ should be multiplied by $($rho$)*$g in order to have pressure units.

Please don't use a matrix approach. Instead, use a node$-$by$-$node one.