Chapter 4, Problem 92P

Consider the general form of the Reynolds transport theorem (RTT) given by $\frac{d{B}_{xys}}{dt}=\frac{d}{dt}{\displaystyle {\int }_{CV}^{}\rho b}dV{\displaystyle {\int }_{cs}^{}\rho b\stackrel{\to }{V},\stackrel{\to }{n}dA}$ Where ${\stackrel{\to }{V}}_r$is the velocity of the fluid relative to the control surface. Let B_sysbe the mass m of a closed system of fluid particles. We know that for a system. Dm/dt = 0 since no mass can enter or leave the system by definition. Use the 2iven equation to derive the equation of conservation of mass for a control volume.