Given:
The length of the drainage pipe, l=18 ft.
The slope of the drainage pope is 1/4 inch of vertical drop per foot of horizontal distance.
Hence, the slope is m=1/4 in/ft.
Now, the vertical drop can be calculated by multipying the slope 1/4 in/ft by the length of pipe.
Thus, the vertical drop needed for a 18 ft pipe is,
[tex]\begin{gathered} x=m\times l \\ =\frac{1}{4}\frac{in}{ft}\times18\text{ ft} \\ =4.5\text{ in} \end{gathered}[/tex]Therefore, the vertical drop needed for a 18 ft pipe is 4.5 in.