$2.$ A Francis turbine is installed with a vertical draft tube is$.$ The top of the draft, tube is $1\mathrm{.}0$ m below the center line of the spiral casing while the tail race $($water level$)$ is $3\mathrm{.}0$ m

from the top of the draft tube. There is no velocity of whirl at the top or bottom of the draft tube and leakage.losses are negligible. The elevation of the water from the reservoir to the center line of the turbine spiral casing is $50\mathrm{.}0$ m$.,$ and water velocity at the inlet is $5\mathrm{.}0$ m$/$s$.$ Discharge is $2\mathrm{.}5$ cubic m$/$s$,$ hydraulic efficiency is $86\%$ and overall efficiency of $83\%.$ Determine the following:

a$.$ the reading of a pressure gage $($in psi$)$ if one is installed at the penstock just before the water inlet to the turbine.

b$.$ the power output of the plant in KW$.$

c$.$ the mechanical efficiency of the turbine.