$1.(10$pts$)$ Water flows in a horizontal constant$-$area pipe; the pipe diameter is $75$ mm$,$ the flow is fully developed, and the average flow speed is $5$ m$/$s$.$ At the pipe inlet, the gage pressure is $275$ kPa, and the outlet is at atmospheric pressure. Consider the density of

water to be p $=1000$ kg$/$m and the gravitational acceleration to be $10$ m$/$s

$$Determine the head loss in the pipe. $(4$pts$)$

$$If the pipe is now aligned so that the outlet is $15$ m above the inlet, what will the inlet pressure need to be to maintain the same flow rate? $(3$pts$)$

$$How much lower than the inlet must the outlet be so that the same flow rate is maintained if both ends of the pipe are at atmospheric pressure $($i$.$e$.,$ gravity feed$)?$

$(3$pts$)$