A pump is put into operation developing a flow rate of $75$m$^(3)//$h of water and a manometric head of $22$ m$,$ with the rotor rotating at $1,500$rpm$.$ The suction and discharge reservoirs are open to the atmosphere. Assuming that this pump is installed $8$ meters above the level of the suction reservoir, determine:

$($a$)$ The value of the vacuum pressure $[$kgf$//$cm$^(2)]$ acting at the pump inlet, considering that the variation in kinetic energy and the pressure loss in the suction can be neglected.

$($b$)$ If a pressure gauge is installed at the pump outlet, placed $60$ cm above the pump level, what should its reading $[$kgf$//$cm$^(2)]$ be for the operating conditions specified above?

$($c$)$ What should the new pressure gauge reading $[$kgf$//$cm$^(2)]$ be if an operator acts on the pump rotation until the flow rate drops by $20\%?$ What is the value of the new pump rotation required for this new condition? $($Assume that the pump performance does not change with this change in its operating condition$).$