The hydraulic fluid volume flow rate is $12\mathrm{.}878\frac{l}{m}in.$

The transmission speed is $8,928\mathrm{.}6rpm.$

The following design specifications apply:

The rear wheel maintains traction at maximum engine power in $5$th gear.

When the rear wheel maintains traction, the pump and the motor are sized for free

wheeling $($no$-$load$)$ of the front wheel.

Transmission sprocket has $18$ teeth.

Pump sprocket has $29$ teeth.

The outer radius of the pump gears is limited to $15$ mm and the width of the gears is

limited to $7\mathrm{.}2$ mm $.$

Determine:

$($a$)$ The pump speed in $rpm.$

$($b$)$ The system pressure in $[$bar$].($Neglect the effect of hydraulic fluid viscosity.$)$

$($c$)$ The displacement volume flow rate of the pump in $[[$l$/$min$].$

$($d$)$ The volumetric efficiency of the pump in $[\%].$

$($e$)$ The displacement volume of the pump in $c{m}^3.$

$($f$)$ The gear pump inner radius in $[$mm$].$