Question $4.[$MEEN$1$A$,$ CLO $2\mathrm{.}4][6$ marks$]$

A $180$ elbow in a horizontal pipe is used to direct water flow upward at a rate of $40k\frac{g}{s}.$ 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 radius of the $180$ elbow is $50$ cm $.$ The weight of the elbow and the water in it is considered to be negligible. Determine the gage pressure at the center of the inlet of the elbow. Take the density of water to be $1000k\frac{g}{m^3}.$