Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows

Doglas Ambani Onchere; Mathew Ngugi Kinyanjui; Phineas Roy Kiogora

doi:doi:10.11648/j.acm.20261501.11

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Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows

Doglas Ambani Onchere^*

, Mathew Ngugi Kinyanjui, Phineas Roy Kiogora

Published in Applied and Computational Mathematics (Volume 15, Issue 1)

Received: 17 October 2025 Accepted: 27 October 2025 Published: 8 January 2026

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Abstract

This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the overall benefits of dam operations by causing tunnel blockages, energy losses, and low discharge conditions. The novelty of this work is to develop a mathematical model that incorporates water-sediment interactions to accurately predict deposition zones, quantify energy dissipation, and support effective sediment management strategies. The governing equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. These equations are transformed from nonlinear partial differential equations into a system of linear ordinary differential equations using similarity transformations. The resulting equations are then solved using the collocation numerical technique and simulated in MATLAB software to obtain the profiles of the flow variables. The flow variables profiles are presented graphically. Flow parameters are varied, and their effects on the flow variables are discussed. It was observed that an increase in both the Reynolds number and the thermal Grashof number leads to an increase in velocity profiles, whereas an increase mass Grashof number produces an opposite effect by reducing the fluid velocity. Temperature of the fluid decreases with increasing Prandtl number, while an increase in the Eckert number leads to higher temperature profiles. The concentration profile decreases as the Schmidt number, Concentration ratio, and thermophoresis parameter increase. The research findings can help in making informed decisions on the in-dam safety, improving sediment management practices, ensuring reliable hydropower generation, and preventing blockage of the pipe. Furthermore, the research contributes to the design of more resilient discharge structures that can efficiently handle sediment, thereby extending the lifespan of hydraulic infrastructure and promoting sustainable operation of dam-driven systems.

Published in	Applied and Computational Mathematics (Volume 15, Issue 1)
DOI	10.11648/j.acm.20261501.11
Page(s)	1-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Dam Break, Sediment-laden Flow, Hydropower Plant, Sediment Deposition Rate, Non-Newtonian Fluid

References

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APA Style

Onchere, D. A., Kinyanjui, M. N., Kiogora, P. R. (2026). Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows. Applied and Computational Mathematics, 15(1), 1-12. https://doi.org/10.11648/j.acm.20261501.11

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ACS Style

Onchere, D. A.; Kinyanjui, M. N.; Kiogora, P. R. Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows. Appl. Comput. Math. 2026, 15(1), 1-12. doi: 10.11648/j.acm.20261501.11

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AMA Style

Onchere DA, Kinyanjui MN, Kiogora PR. Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows. Appl Comput Math. 2026;15(1):1-12. doi: 10.11648/j.acm.20261501.11

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@article{10.11648/j.acm.20261501.11,
  author = {Doglas Ambani Onchere and Mathew Ngugi Kinyanjui and Phineas Roy Kiogora},
  title = {Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows
},
  journal = {Applied and Computational Mathematics},
  volume = {15},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.acm.20261501.11},
  url = {https://doi.org/10.11648/j.acm.20261501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20261501.11},
  abstract = {This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the overall benefits of dam operations by causing tunnel blockages, energy losses, and low discharge conditions. The novelty of this work is to develop a mathematical model that incorporates water-sediment interactions to accurately predict deposition zones, quantify energy dissipation, and support effective sediment management strategies. The governing equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. These equations are transformed from nonlinear partial differential equations into a system of linear ordinary differential equations using similarity transformations. The resulting equations are then solved using the collocation numerical technique and simulated in MATLAB software to obtain the profiles of the flow variables. The flow variables profiles are presented graphically. Flow parameters are varied, and their effects on the flow variables are discussed. It was observed that an increase in both the Reynolds number and the thermal Grashof number leads to an increase in velocity profiles, whereas an increase mass Grashof number produces an opposite effect by reducing the fluid velocity. Temperature of the fluid decreases with increasing Prandtl number, while an increase in the Eckert number leads to higher temperature profiles. The concentration profile decreases as the Schmidt number, Concentration ratio, and thermophoresis parameter increase. The research findings can help in making informed decisions on the in-dam safety, improving sediment management practices, ensuring reliable hydropower generation, and preventing blockage of the pipe. Furthermore, the research contributes to the design of more resilient discharge structures that can efficiently handle sediment, thereby extending the lifespan of hydraulic infrastructure and promoting sustainable operation of dam-driven systems.
},
 year = {2026}
}

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TY  - JOUR
T1  - Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows

AU  - Doglas Ambani Onchere
AU  - Mathew Ngugi Kinyanjui
AU  - Phineas Roy Kiogora
Y1  - 2026/01/08
PY  - 2026
N1  - https://doi.org/10.11648/j.acm.20261501.11
DO  - 10.11648/j.acm.20261501.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20261501.11
AB  - This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the overall benefits of dam operations by causing tunnel blockages, energy losses, and low discharge conditions. The novelty of this work is to develop a mathematical model that incorporates water-sediment interactions to accurately predict deposition zones, quantify energy dissipation, and support effective sediment management strategies. The governing equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. These equations are transformed from nonlinear partial differential equations into a system of linear ordinary differential equations using similarity transformations. The resulting equations are then solved using the collocation numerical technique and simulated in MATLAB software to obtain the profiles of the flow variables. The flow variables profiles are presented graphically. Flow parameters are varied, and their effects on the flow variables are discussed. It was observed that an increase in both the Reynolds number and the thermal Grashof number leads to an increase in velocity profiles, whereas an increase mass Grashof number produces an opposite effect by reducing the fluid velocity. Temperature of the fluid decreases with increasing Prandtl number, while an increase in the Eckert number leads to higher temperature profiles. The concentration profile decreases as the Schmidt number, Concentration ratio, and thermophoresis parameter increase. The research findings can help in making informed decisions on the in-dam safety, improving sediment management practices, ensuring reliable hydropower generation, and preventing blockage of the pipe. Furthermore, the research contributes to the design of more resilient discharge structures that can efficiently handle sediment, thereby extending the lifespan of hydraulic infrastructure and promoting sustainable operation of dam-driven systems.

VL  - 15
IS  - 1
ER  -

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Author Information

Doglas Ambani Onchere

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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http://orcid.org/0009-0004-9534-948X
Mathew Ngugi Kinyanjui

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

Contact Email
Phineas Roy Kiogora

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

Contact Email

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APA Style

Onchere, D. A., Kinyanjui, M. N., Kiogora, P. R. (2026). Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows. Applied and Computational Mathematics, 15(1), 1-12. https://doi.org/10.11648/j.acm.20261501.11

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ACS Style

Onchere, D. A.; Kinyanjui, M. N.; Kiogora, P. R. Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows. Appl. Comput. Math. 2026, 15(1), 1-12. doi: 10.11648/j.acm.20261501.11

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AMA Style

Onchere DA, Kinyanjui MN, Kiogora PR. Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows. Appl Comput Math. 2026;15(1):1-12. doi: 10.11648/j.acm.20261501.11

Copy | Download

@article{10.11648/j.acm.20261501.11,
  author = {Doglas Ambani Onchere and Mathew Ngugi Kinyanjui and Phineas Roy Kiogora},
  title = {Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows
},
  journal = {Applied and Computational Mathematics},
  volume = {15},
  number = {1},
  pages = {1-12},
  doi = {10.11648/j.acm.20261501.11},
  url = {https://doi.org/10.11648/j.acm.20261501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20261501.11},
  abstract = {This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the overall benefits of dam operations by causing tunnel blockages, energy losses, and low discharge conditions. The novelty of this work is to develop a mathematical model that incorporates water-sediment interactions to accurately predict deposition zones, quantify energy dissipation, and support effective sediment management strategies. The governing equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. These equations are transformed from nonlinear partial differential equations into a system of linear ordinary differential equations using similarity transformations. The resulting equations are then solved using the collocation numerical technique and simulated in MATLAB software to obtain the profiles of the flow variables. The flow variables profiles are presented graphically. Flow parameters are varied, and their effects on the flow variables are discussed. It was observed that an increase in both the Reynolds number and the thermal Grashof number leads to an increase in velocity profiles, whereas an increase mass Grashof number produces an opposite effect by reducing the fluid velocity. Temperature of the fluid decreases with increasing Prandtl number, while an increase in the Eckert number leads to higher temperature profiles. The concentration profile decreases as the Schmidt number, Concentration ratio, and thermophoresis parameter increase. The research findings can help in making informed decisions on the in-dam safety, improving sediment management practices, ensuring reliable hydropower generation, and preventing blockage of the pipe. Furthermore, the research contributes to the design of more resilient discharge structures that can efficiently handle sediment, thereby extending the lifespan of hydraulic infrastructure and promoting sustainable operation of dam-driven systems.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Study of Coupled Water-Sediment Energy Dynamics in Dam-Driven Closed-Conduit Flows

AU  - Doglas Ambani Onchere
AU  - Mathew Ngugi Kinyanjui
AU  - Phineas Roy Kiogora
Y1  - 2026/01/08
PY  - 2026
N1  - https://doi.org/10.11648/j.acm.20261501.11
DO  - 10.11648/j.acm.20261501.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20261501.11
AB  - This study examines the coupled water-sediment energy dynamics in dam-driven closed-conduit flows, aiming to forecast discharge capacity and optimize release strategies for water supply, flood control, and hydropower generation. Sediment accumulation within dams significantly reduces hydraulic efficiency, limits the water supply, and undermines the overall benefits of dam operations by causing tunnel blockages, energy losses, and low discharge conditions. The novelty of this work is to develop a mathematical model that incorporates water-sediment interactions to accurately predict deposition zones, quantify energy dissipation, and support effective sediment management strategies. The governing equations are the continuity equation, the momentum equation, the energy equation, and the concentration equation. These equations are transformed from nonlinear partial differential equations into a system of linear ordinary differential equations using similarity transformations. The resulting equations are then solved using the collocation numerical technique and simulated in MATLAB software to obtain the profiles of the flow variables. The flow variables profiles are presented graphically. Flow parameters are varied, and their effects on the flow variables are discussed. It was observed that an increase in both the Reynolds number and the thermal Grashof number leads to an increase in velocity profiles, whereas an increase mass Grashof number produces an opposite effect by reducing the fluid velocity. Temperature of the fluid decreases with increasing Prandtl number, while an increase in the Eckert number leads to higher temperature profiles. The concentration profile decreases as the Schmidt number, Concentration ratio, and thermophoresis parameter increase. The research findings can help in making informed decisions on the in-dam safety, improving sediment management practices, ensuring reliable hydropower generation, and preventing blockage of the pipe. Furthermore, the research contributes to the design of more resilient discharge structures that can efficiently handle sediment, thereby extending the lifespan of hydraulic infrastructure and promoting sustainable operation of dam-driven systems.

VL  - 15
IS  - 1
ER  -

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