An underground mine development project has a $560$ m shaft sinking whose diameter is $5$ m; three sublevel tunnels planned at $440$m$,500$m and $560$m$,$ respectively; and a decline to the $560$ m level. The decline $($cross section $5$ m x $5\mathrm{.}6$ m$)$ development has reached the $500$ m level, and the tunnel $($cross section $5$ m x $5\mathrm{.}6$ m$)$ development at the $440$ m level has extended $200$ m towards the shaft direction. Unfortunately, the decline development at the $500$ m encountered major groundwater inrush and flooded the entire decline and the $440$ m level tunnel. An overflow of $50$ m$3/$hour is measured at the portal of the decline. Design a pumping system to dewater the flooded mine developments.

To complete the design, your design report shall cover the following three components:

$1)$ Overall pump stages of the pipeline and pumping system, including:

$$ the overall pumping strategy to pump the water from underground to ground surface,

$$ your own layout design drawing, and

$$ total pipeline length.

$2)$ How long will it take to dewater the flooded space? Assume that the pump has an efficiency of $90\%.$ Detail any other assumptions used in the design and calculation.

$3)$ Pumping system design and pump selection, including:

$$ Design an adequate pumping system to meet the pumping requests, e$.$g$.$ discharge rate and the elevation request.

$$ Select a pump, including brand name, model and capacity