Consider the differential element $($or control volume$)$ of static fluid, derive the relationship of between the fluid pressure and the position $(x,y,z)$ given by the following conditions: a$)$ the density of the fluid within the element is constant; b$)$ the pressure at the center of the element is p and that the dimensions of the element are $x,y,$ and $z.$

Prove that the difference between the rate of change of $x($e$.$g$.,$ mass$)$ within the system and that within the control volume is equal to the net rate of outflow from the control volume, i$.$e$.,\frac{d{x}_s}{dt}=\frac{d{x}_{CV}}{dt}+\frac{d{x}_{CV}^{\text{o}\text{u}\text{t}}}{dt}-\frac{d{x}_{CV}^{in}}{dt},$ where the subscript S represents the fluid system, the subscript CV is the control volume

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