Neco Model Questions Vol1 2019 Geography Question 48

A small catchment of \(2.5\ \text{km}^2\) has a runoff coefficient of 0.45. The design storm is a 30‑year event with a rainfall intensity of \(85\ \text{mm\,h}^{-1}\) for a duration equal to the time of concentration. The length of the main channel is \(1\,500\ \text{m}\) and its average slope is \(0.02\).\n\n(a) Estimate the time of concentration (in minutes) using the Kirpich formula \(T_c = 0.0195\,L^{0.77}S^{-0.385}\).\n(b) Compute the peak discharge \(Q\) (in \(\text{m}^3\text{s}^{-1}\)) using the rational method \(Q = 0.278\,C\,i\,A\).\n(c) Assuming a circular pipe conveys the runoff at full flow, with Manning's \(n = 0.013\) and pipe slope \(0.001\), determine the required pipe diameter (in metres, to one decimal place).