Manning's equation is an empirical formula for estimating the average velocity of an open channel flow. In a rectangular channel it can be expressed as Q 1 (BH) 5/3 √s n(B + 2H)2/3 where Q = flow rate (m³/s), n = roughness coefficient, B = width (m), H= depth (m), and S = slope. You are applying this formula to a stream where you know that the width = 20 m and the depth = 0.3 m. Unfortunately, you know the roughness and the slope to only a± 10% precision. That is, you know that the roughness is about 0.03 with a range from 0.027 to 0.033 and the slope is 0.0003 with a range from 0.00027 to 0.00033. Use a first-order error analysis to determine the sensitivity of the flow prediction to each of these two factors. Which one should you attempt to measure with more precision?