In the given problem, it involves the design of a vertical Thermosyphon reboiler, taken from the bookCoulson and Richardsons Chemical Engineering Series, Chemical Engineering Design, Sixth Edition byRay Sinnott and Gavin Towler. Example $12\mathrm{.}11($page$747)$ Can be found on the internet.

During the calculation of the driving force for the circulation of the substance from the bottom of the distillation column into the Thermosyphon Reboiler.

In the calculation of the pressure drop due to friction in the reboiler tubes $(\backslash$Delta Pf$),$ he calculated $(\backslash$Delta Pf$/$L$)$ at the inlet and the outlet, and then assumed the value to be a linear function with the length of the tube. Explain the reason why he did this, providing detailed calculations as well.