Problem C$2$

The figure below shows a fixed control volume. It has a volume $Y_0{?}_0=1\mathrm{.}0f{t}^3,$ a flow area

$A=1\mathrm{.}0f{t}^2,$ and a length $l_0=1\mathrm{.}0ft.$ Position $x$ represents the center of the control volume

where the fluid velocity $V_0=1\mathrm{.}0f\frac{t}{s}$ and the density ${}_0=1\mathrm{.}800$slu$\frac{g}{f}{t}^3.$ Also, at position $x,$

the fluid density does not change locally with time but decreases in the axial direction at the

linear rate of $0\mathrm{.}25$ slug$/f{t}^4.$ Find $\frac{DV}{Dt}$ for the system.