Question $4$: Drainage Design

a$.$ Explain the significance of drainage design in road construction. Discuss the effects of inadequate drainage on road performance.

b$.$ Design a side ditch for a rural road with the following conditions:

Road longitudinal slope: $2\%$

Cross slope: $2\mathrm{.}5\%$

Rainfall intensity: $50m\frac{m}{h}r$

Runoff coefficient: $0\mathrm{.}9$

Width of the road surface: $7\mathrm{.}5$ meters

Calculate the required dimensions of the side ditch to effectively channel runoff water.