The following design specifications apply:

The engine speed is $8500$ rpm $.$

The transmission is in $5^{th}$ gear where the speed reduction ratio between the engine

and the transmission output is $0\mathrm{.}952.($The transmission output turns faster than

the engine$).$

The speed reduction ratio between the transmission output and the rear wheel is

$3\mathrm{.}85.($The rear wheel turns slower than the transmission output.$)$

The rear wheel diameter is $675$ mm and the front wheel diameter is $695$ mm $.$

Flow in the hydraulic lines $($flexible hoses and pipes$)$ remains laminar $(Re<mn>2</mn><mn>3</mn><mn>0</mn><mn>0</mn><mtext></mtext><mi>)</mi>$

up to an engine speed of $8500$ rpm $.$

The kinematic viscosity of a hydraulic fluid is $12\mathrm{.}5$ cSt $.$

The inner diameter of the hydraulic lines $($except for the pump inlet line$)$ is $\frac{3}{8}$ inch

$(9\mathrm{.}52mm)$

Determine:

$($a$)$ The hydraulic fluid flow velocity in $\frac{m}{s}.$

$($b$)$ The hydraulic fluid volume flow rate in $\frac{l}{m}in.$

$($c$)$ The transmission speed in $[$rpm$].$

$($d$)$ The rear wheel speed $[$rpm$].$

$($e$)$ The front wheel speed when the rear wheel maintains traction, in $[$rpm$].$