A drilling rig $($n $=8$ lines$)$ is working at an elevation of $2500$ft with a draw works efficiency of $90\%.$ The peak temperature is $110$ degress daytime. The rig has three $1,000$hp prime movers. A drill string consisting of $600$ drill pipe joints $(30$ft each, $21\mathrm{.}5$ Ib$/$ft weight$)$ is lowered inside the wellbore $($mud density is $10\mathrm{.}5$ppg$)$ Determine

$1.$ Hook Horsepower

$2.$ Fastline speed

$3.$ Fastline tension

$4.$ Static line tension

$5.$ Derrick load

$6.$ Load on each leg

$7.$ Maximum equivalent derrick load and derrick efficiency

$8.$ Drum speed if its diameter is $32$ in