Problem $1(2\mathrm{.}5$ points$)$: The tank shown in the Figure below is being filled with water by two one$-$

dimensional inlets. Air is trapped at the top of the tank. The water height is $h.($a$)$ Find an expression for the

rate of change of water height $d\frac{h}{d}t.($b$)$ Compute $d\frac{h}{d}t$ if $D_1=1in,D_2=3in,V_1=3f\frac{t}{s},V_2=2f\frac{t}{s},$ and tank

area $A_t=2f{t}^2,$ assuming water at $20C.($c$)$ if the top of the tank is open, does dh$/$dt increase or decrease?