Field observations are carried out to assess the discharge of a river. Measurements are taken in a 2000 m straight reach. Slope is approximately 1 in 4000. Bed slope is determinably to a possible accuracy of 0.4 cm; wetted perimeter is determinable within 4% of possible error; and sectional area within 6% of possible error. Using Chezy’s equation, the assessed discharge will be accurate to within

Concept:Chezzy’s equation can be WRITTEN as,\(Q = A \times C\sqrt {RS} \)\(Q= A \times C \times \sqrt {\frac{A}{P}} \times S\)Q = A3/2 × C × P-1/2 × SWhere, Q = discharge, A = AREA of flow, P = wetted perimeter of flow & S = slope of the channel\(\frac{{dQ}}{{DA}} = \frac{3}{2} \times {A^{1/2}} \times C \times {P^{ - 1/2}} \times 5 \Rightarrow dQ = \frac{3}{2} \times \sqrt A \times \frac{C}{{\sqrt P }} \times 5 \times dA\)\(\frac{{dQ}}{Q} = \frac{3}{2} \times \frac{{dA}}{A}\)Similarly for perimeter,\(\frac{{dQ}}{Q} = \frac{1}{2} \times \frac{{dP}}{P}\) & for slope, \(\frac{{dQ}}{Q} = \frac{1}{2} \times \frac{{dS}}{S}\)Overall change in %\(\frac{{dQ}}{Q} \times 100 = \frac{3}{2} \times \frac{{dA}}{A} \times 100 + \frac{1}{x} \times \frac{{dP}}{P} \times 100 + \frac{1}{2} \times \frac{{dS}}{S} \times 100\)Calculation:L = 2000 m, Slope = 1/4000% error in slope \(= \frac{{0.4}}{{\left( {\frac{{2000}}{{4000}}} \right) \times 100}} \times 100 = 0.8\% \) Possible error in wetted perimeter = 4%Possible error in area = 6%\(\frac{{dQ}}{Q} \times 100 = \frac{3}{2} \times 6 + \frac{1}{2} \times 4 + \frac{1}{2} \times 0.8 = 9 + 2 + 0.4 = 11.4\% \)