Problem $1$ After a big, cold $(T=10C)$ rainstorm, water fills a foundation at a construction site. In order to

keep the project on schedule, you must figure out a way to pump the water out of the foundation in one day.

Additionally, in order to legally discharge the water, you must remove sediment using a filter. You propose the

below setup, with a filter placed midway along the pipe and a pump at the top of the hill near the discharge

location.

$1\mathrm{.}1$ If you must empty the foundation pit in one day $(24hrs),$ what average flow rate is required?

$1\mathrm{.}2$ If the pump generates this flow, how much head must the pump add in order to generate this flow rate?

Neglect the small entrance loss.

$1\mathrm{.}3$ Based on these calculations, perform an accounting of the flow energy from beginning to end $($beginning

energy, where energy is lost and gained, etc.$)$ below:

Initial energy $(m)$ :

Major losses $($m$)$:

Minor losses $($m$)$:

Pump $($m$)$:

Final Energy $($m$)$: