Page 1 Lecture 4: Hydraulic routing Module 5 Page 2 Lecture 4: Hydraulic routing Module 5 Hydraulic/Distributed flow routing ? Flow is calculated as a function of space and time throughout the system ? Hydraulic methods use continuity and momentum equation along with the equation of motion of unsteady flow (St. Venant equations). ? St. Venant Equations (Refer to Module 6 for more details) ? Kinematic wave routing ? Diffusion wave routing ? Muskingum-Cunge method ? Dynamic wave routing Module 5 Page 3 Lecture 4: Hydraulic routing Module 5 Hydraulic/Distributed flow routing ? Flow is calculated as a function of space and time throughout the system ? Hydraulic methods use continuity and momentum equation along with the equation of motion of unsteady flow (St. Venant equations). ? St. Venant Equations (Refer to Module 6 for more details) ? Kinematic wave routing ? Diffusion wave routing ? Muskingum-Cunge method ? Dynamic wave routing Module 5 It is the relationship between the Muskingum method and the Saint-Venant equations. Inflow-Outflow Equation: The constants C 0 , C 1 and C 2 are functions of wave celerity, c. Q ?discharge and y ? depth of flow Muskingum-Cunge method Diffusion wave routing Module 5 , dy dA dy dQ dA dQ c = = t O I I O 2 1 0 C C C t t t t t + + = ? + ? + Page 4 Lecture 4: Hydraulic routing Module 5 Hydraulic/Distributed flow routing ? Flow is calculated as a function of space and time throughout the system ? Hydraulic methods use continuity and momentum equation along with the equation of motion of unsteady flow (St. Venant equations). ? St. Venant Equations (Refer to Module 6 for more details) ? Kinematic wave routing ? Diffusion wave routing ? Muskingum-Cunge method ? Dynamic wave routing Module 5 It is the relationship between the Muskingum method and the Saint-Venant equations. Inflow-Outflow Equation: The constants C 0 , C 1 and C 2 are functions of wave celerity, c. Q ?discharge and y ? depth of flow Muskingum-Cunge method Diffusion wave routing Module 5 , dy dA dy dQ dA dQ c = = t O I I O 2 1 0 C C C t t t t t + + = ? + ? + where, Q 0 = Reference discharge, S 0 = Reach Slope, Q B = Baseflow Q p = Peak flow taken from the inflow hydrograph Module 5 Muskingum-Cunge method Contd… Diffusion wave routing ? ? ? ? ? ? ? ? ? - = x S T c Q X * * * 1 2 1 0 0 ( ) B p B Q Q Q Q - + = 50 . 0 0 Page 5 Lecture 4: Hydraulic routing Module 5 Hydraulic/Distributed flow routing ? Flow is calculated as a function of space and time throughout the system ? Hydraulic methods use continuity and momentum equation along with the equation of motion of unsteady flow (St. Venant equations). ? St. Venant Equations (Refer to Module 6 for more details) ? Kinematic wave routing ? Diffusion wave routing ? Muskingum-Cunge method ? Dynamic wave routing Module 5 It is the relationship between the Muskingum method and the Saint-Venant equations. Inflow-Outflow Equation: The constants C 0 , C 1 and C 2 are functions of wave celerity, c. Q ?discharge and y ? depth of flow Muskingum-Cunge method Diffusion wave routing Module 5 , dy dA dy dQ dA dQ c = = t O I I O 2 1 0 C C C t t t t t + + = ? + ? + where, Q 0 = Reference discharge, S 0 = Reach Slope, Q B = Baseflow Q p = Peak flow taken from the inflow hydrograph Module 5 Muskingum-Cunge method Contd… Diffusion wave routing ? ? ? ? ? ? ? ? ? - = x S T c Q X * * * 1 2 1 0 0 ( ) B p B Q Q Q Q - + = 50 . 0 0 Dynamic Wave Routing Flow in natural channels is unsteady, non-uniform with junctions, tributaries, variable cross-sections, variable resistances, variable depths, etc. The complete St.Venant equation represents the dynamic wave routing. (Refer to Module 6 for more details) Valley storage Prism storage Wedge storage Non-conservative form of continuity equation Module 5 ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? + ? ? = x y V x V y t y 0Read More

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