A hydraulic system in an industrial plant involves the transportation of hydraulic oil through a network of pipes. The initial pipe has a diameter of $120$ mm$,$ and the oil flows at a rate of $0\mathrm{.}08$ m$^3/$s$.$The pipe then expands suddenly to a diameter of $240$ mm$.$ The pressure intensity in the smaller pipe is$12\mathrm{.}5$ N$/$ cm$^2.$ The hydraulic system is critical for the efficient operation of heavy machinery.Calculate:$($i$)$ Loss of head due to sudden enlargement. $($ii$)$ Power lost due to enlargement. $($iii$)$ Pressure intensity in the larger pipe.