In the given problem, it involves the design of a vertical Thermosyphon reboiler, taken from the book Coulson and Richardson$$s Chemical Engineering Series, Chemical Engineering Design, Sixth Edition by Ray Sinnott and Gavin Towler. Example $12\mathrm{.}11($page $747)$

Consider the tube in the reboiler along with the bottom column of the distillation column as a system. Then, apply the mechanical energy balance learned to prove the conclusion that the available head of the system is sufficient to maintain the circulation rate by overcoming the pressure drop due to the friction in the tube as well as the static pressure of the fluid in the reboiler. The mechanical energy balance equation to be used as shown equation. ${\displaystyle \underset{1}{\overset{2}{}}}\frac{1}{}dP+(\frac{v_2^2-v_1^2}{2g_c})+(\frac{g}{g_c}(Z_2-Z_1))+{\displaystyle \underset{?}{\overset{?}{}}}{F}_f+W_s=0$

Draw the system and designate positions $1$ and $2$ in order to apply this mechanical energy balance, along with the assumptions that need to be used in the proof.