Required information

A $\backslash (90^\{\backslash$circ$\}\backslash )$ elbow in a horizontal pipe is used to direct water flow upward at a rate $\backslash ($ m $\backslash )$ of $\backslash (35\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The diameter of the entire elbow is $10$ cm $.$ The elbow discharges water into the atmosphere, and thus the pressure at the exit is the local atmospheric pressure. The elevation difference between the centers of the exit and the inlet of the elbow is $50$ cm $.$ The weight of the elbow and the water in it is considered to be negligible. Take the density of water to be $\backslash (1000\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and the momentum$-$flux correction factor to be $1\mathrm{.}03$ at both the inlet and the outlet.

Determine the gage pressure at the center of the inlet of the elbow.

The gage pressure at the center of the inlet of the elbow is kPa.