An estimation of discharge using mean velocity derived through Chiu’s velocity equation

Derivation of Equation for Mean Suspended Sediment Based on Probabilistic Concept

“…Using (11) The above approach is a method that was utilized in velocity calculation through the velocity entropy maximization concept by [6], which was also applied to the sediment concentration equivalently.…”

“…One of the widely known distribution formulas of suspended sediments concentration is Rouse concentration distribution formula [6] as below: (1) where c refers to a concentration, a c refers to a distance, a y  refers to a sediment concentration, Z refers to * s u / ω  , s  refers to a particle sedimentation velocity,  refers to a coefficient,  refers to von Karman constant, * u refers to shear velocity, and D refers to a water depth.…”

“…Therefore, the present study proposed a formula that can calculate a mean sediment concentration by simplifying parameters as much as possible. The detailed elicitation process in the calculation formula of velocity distribution and mean velocity, which are required to understand the calculation formula of mean sediment concentration using the probabilistic entropy concept, are found in the previous studies done by Chiu and Choo so they were omitted in this paper [4], [6], [11]- [14].…”

“…The constraints for the formula are as follows [15]. In order to calculate a mean sediment concentration formula, (8) is plugged into (5), (6), and (7) and arranged to produce (9) and (10). …”

“…In order to calculate the sediment equilibrium state, it is necessary to calculate a k value that represents a ratio of sediment concentration between bottom and water surface. To achieve this, the following (11) [6]. Finally, sediment distribution can be estimated by using (14).…”