$3\mathrm{.}4\mathrm{.}7$ Figure P$3\mathrm{.}4\mathrm{.}7$ shows a fixed control volume. It has a volume $A{A}_0=0\mathrm{.}028m^3,$ a flow area $A=0\mathrm{.}09m^2,$ and a length $l_0=0\mathrm{.}3m.$ Position $x$ represents the center of the control volume, where the fluid velocity $V_0=0\mathrm{.}3\frac{m}{s}$ and the density ${}_0=927\mathrm{.}7k\frac{g}{m^3}.$ Also, at position $x$ the fluid density does not change locally with time but decreases in the axial direction at the linear rate of $450\mathrm{.}6k\frac{g}{m^4}.$ Use the system or Lagrangian approach to evaluate $d\frac{}{d}t.$ Compare this result with that of the material derivative and flux terms. ort