A centrifugal pump impeller has external diameter and width at outlet of $800$ mm and $100$ mm respectively while it runs at $550$ rpm$.$ The angle of the impeller vanes at the outlet is $40\backslash$deg $.$ The pump delivers $0\mathrm{.}98$ m$^2$ of water per second under an effective head of $35$ m$.$ If the pump is driven by a $500$ kW motor determine: $($i$)$ manometric efficiency, $($ii$)$ overall efficiency and $($illi$)$ mechanical efficiency.