rectangular canal. It was developed by the Irish engineer Robert Manning in the $19$th century based on a best$-$fit of observed and measured data sets. You are provided the following values for the four variables in Manning's equation, and their respective error in the table below.

$Q=\frac{1}{n}\frac{(BH{)}^{\frac{5}{3}}}{(B+2H{)}^{\frac{2}{3}}}\sqrt[\phantom{2}]{S}$

Based on the information given above, answer the following:

$($a$)$ Is the Manning equation mechanistic or empirical model?

$($b$)$ What is the value for the flow rate, $Q,$ in $\frac{m^3}{s},$ using the given values in the table above? Provide the answer with the appropriate significant figures.

$($c$)$ What is the total error in the calculated flow rate, Q$,$ based on the error in the individual variables provided in the table? Give the answer in $\frac{m^3}{s}$ and $\%$ of the answer obtained in $b.$

Note: You may use the internet or other resources to find the partial derivative equations.

$($d$)$ Which of the variables has the biggest impact on the error for the flow rate, Q$?$ Explain the implications. $3-$ Manning's equation can be used to predict the flow in a