SE$115$ Final $1$ NAME: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ SCORE:$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$1.$ As shown in the following figure, a water turbine is installed to extract energy from the incoming flow. We assume that the flow is uniform at both the inlet and the outlet. We know: the density of fluid $$; the area of the inlet$1$Aand that of the outlet $2$ A ; the pressure at the inlet $(1$p$)$ and that of the outlet $(2$ p$)$ are different; and the flow