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%\(\frac{{dQ}}{Q} \times 100 = \frac{3}{2} \times 6 + \frac{1}{2} \times 4 + \frac{1}{2} \times 0.8 = 9 + 2 + 0.4 = 11.4\% \)

"> 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%\(\frac{{dQ}}{Q} \times 100 = \frac{3}{2} \times 6 + \frac{1}{2} \times 4 + \frac{1}{2} \times 0.8 = 9 + 2 + 0.4 = 11.4\% \)

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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

Fluid Mechanics Open Channel Flow in Fluid Mechanics . 6 months ago

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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%\(\frac{{dQ}}{Q} \times 100 = \frac{3}{2} \times 6 + \frac{1}{2} \times 4 + \frac{1}{2} \times 0.8 = 9 + 2 + 0.4 = 11.4\% \)

Posted on 27 Nov 2024, this text provides information on Fluid Mechanics related to Open Channel Flow in Fluid Mechanics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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