(Solved): Q4. For determining the flow capacity of a wide rectangular water channel, Manning's equation can b ...

Q4. For determining the flow capacity of a wide rectangular water channel, Manning's equation can be written as follows: $Q=n^{?1}{y}^{5/3}{s}^{1/2}$ where; $\mathbf{Q}$ is the flow rate (in ${\mathrm{m}}^3/\mathrm{s}$ ), $\mathbf{n}$ is the roughness coefficient, $\mathbf{y}$ is the water depth (in m), and $\mathbf{S}$ is the slope of the channel. Due to various sources of uncertainties, roughness coefficient, water depth and channel slope are modeled with the following statistical properties as given in the table below. Assuming that these three random variables are statistically independent; a) Using the first-order approximation, estimate the mean and standard deviation of the flow capacity of the channel. b) Assuming that the flow capacity of the channel follows lognormal distribution with the mean and standard deviation obtained from part (a), find the probability that the channel fails in accommodating an inflow of 12 ${\mathrm{m}}^3/\mathrm{s}$.