Page - 428 - in Book of Full Papers - Symposium Hydro Engineering

Fig. 3: Variation of Sediment Concentration and Discharge The proposed equation (13) is of second order. It envelops 94 % of the sediment data at one hundred percent band width, it is also seen that 63% of the sediment data at fifty percent band width, which is shown in Fig. 3. Steady state flow equations which are compared with the observed data are tabulated in table2 given below: Table:2. Prediction of Sediment for Steady State Flow Equations S No. Method/law Predicted Sediment ton Present Studies Steady State Flow Equations 1. Log-log plot 5e 0.05 ln Q Method 316959.32 2. Quadratic 0.0005Q2 - 0.2Q+ 125 Method 297696.70 3. Power 700Q-0.9 127052.40 Observed 119607.29 (B) Unsteady State Flow Equation: As in the de St. Venant equations, x represents a boundary attached downstream coordinate. The equation of sediment continuity was first delineated by the Austrian researcher Exner at the beginning of the 20th century, First a one dimensional case is considered Sediment mass balance is expressed in volume form (by dividing the mass balance by ρs) below; (1−𝜆 𝑝 ) 𝜕 𝜂 𝜕 𝑡 =− 𝜕 𝑞 𝑏 𝑠 𝜕 𝑥 − 𝜕 𝑞 𝑏 𝑚 𝜕 𝑛 +𝜈 𝑠 (𝑐 ?̅? −𝐸 𝑠 ) (14) In the above equation (14) λp denotes the porosity of the bed deposit qbm and qbs. cb denotes the volume concentration of suspended sediment, averaged over turbulence, just above the bed. Es is sediment entrainment into suspension. Bed- load is seen to act as a flux term and suspended sediment as a source/sink term. The bed elevation of a control volume increases if more bed-load is entering than exiting, resulting in net deposition of bed-load. Noting that vs denotes the volume flux of suspended sediment settling on to the bed and vs E denotes the volume flux of entrainment of bed sediment into suspension, bed elevation increases due to the net deposition of suspended sediment. If 𝑐 ?̅? > 𝐸 𝑠 . When the length scales of interest are large compared to the relaxation distance (U/vs) H associated with the settling of suspended sediment, (12) can be rigorously reduced to a simpler form, (1−𝜆 𝑝 )𝐵 𝜕 𝜂 𝜕 𝑡 =− 𝜕 𝑞 𝑡 𝜕 𝑥 (15) For the homogeneous unsteady flow neglecting viscous diffusion and including buoyancy effect the rate of change of sediment concentration (ed. Garcia 2007) is: 428