A single acting reciprocating pump has a $20$cm piston with a crank of radius $40$ cm$.$ The delivery pipe is $10$ cm diameter and $45$ m long. Water is lifted to a height of $40$ m above the axis of the cylinder. Find the maximum speed at which pump can be run without cavitation. Assume atmospheric pressure $9\mathrm{.}75$ m water $($abs$)$ and cavitation occurs at $2\mathrm{.}75$ m water $($abs$).$