(Solved): Consider the cylindrical tank shown in the figure. Identify the dynamic model of the height \( h \ ...

Consider the cylindrical tank shown in the figure. Identify the dynamic model of the height \( h \), assuming that the input mass flow rate is \( q_{m}(t) \) Multiple Choice \[ \frac{1}{\rho 2 L} \sqrt{D h-h^{2}} \frac{\mathrm{d} h}{\mathrm{~d} t}=q_{m} \] \[ \frac{1}{\rho 2 L} \sqrt{D h+h^{2} \frac{\mathrm{d} h}{\mathrm{~d} t}}=q_{m} \] \[ \rho 2 L \sqrt{D h+h^{2}} \frac{\mathrm{d} h}{\mathrm{~d} t}=q_{m} \] \[ \rho 2 L \sqrt{D h-h^{2}} \frac{\mathrm{d} h}{\mathrm{~d} t}=q_{m} \]