TY - JOUR
T1 - Maximum Shear-Stress Method for Stable Channel Design
AU - Patel, Narendra
AU - Mohebbi, Amin
AU - Jan, Chyan Deng
AU - Guo, Junke
N1 - Funding Information:
This research was supported by a Water for Food Institute Fellowship at the University of Nebraska-Lincoln and the add-on Grant (MOST 107-2625-M-006-022) of the Ministry of Sciences and Technology (MOST) in Taiwan.
Publisher Copyright:
© 2020 American Society of Civil Engineers.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Stable channel design is important for conveying water among stakeholders in a safe and cost-effective manner. The current design methods include the regime theory, the permissible velocity method, and the tractive force method. Nevertheless, they are not yet conclusive, despite decades of study, because of difficulties in finding the maximum bed and sidewall shear stresses from the Navier-Stokes equation. To advance stable channel design, we assume a constant eddy viscosity and apply Leighly's conformal mapping idea to the Navier-Stokes equations in rectangular open channel flow, which results in analytic solutions for the bed and sidewall shear stress distributions, including the maximum bed and sidewall shear stresses. We then modify the maximum bed and sidewall shear stress equations with data and apply the resulting equations for stable channel design. We demonstrate that in terms of the regime theory or the tractive force method, the channel geometry parameters (slope, width, and depth) can be theoretically solved by combining the two maximum shear stress equations and Manning's equation for uniform flow.
AB - Stable channel design is important for conveying water among stakeholders in a safe and cost-effective manner. The current design methods include the regime theory, the permissible velocity method, and the tractive force method. Nevertheless, they are not yet conclusive, despite decades of study, because of difficulties in finding the maximum bed and sidewall shear stresses from the Navier-Stokes equation. To advance stable channel design, we assume a constant eddy viscosity and apply Leighly's conformal mapping idea to the Navier-Stokes equations in rectangular open channel flow, which results in analytic solutions for the bed and sidewall shear stress distributions, including the maximum bed and sidewall shear stresses. We then modify the maximum bed and sidewall shear stress equations with data and apply the resulting equations for stable channel design. We demonstrate that in terms of the regime theory or the tractive force method, the channel geometry parameters (slope, width, and depth) can be theoretically solved by combining the two maximum shear stress equations and Manning's equation for uniform flow.
KW - Conformal mapping
KW - Maximum shear stress
KW - Open channel flow
KW - Regime theory
KW - Stable channel analysis
KW - Tractive force method
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U2 - 10.1061/(ASCE)HY.1943-7900.0001827
DO - 10.1061/(ASCE)HY.1943-7900.0001827
M3 - Article
AN - SCOPUS:85092623816
SN - 0733-9429
VL - 146
JO - American Society of Civil Engineers, Journal of the Hydraulics Division
JF - American Society of Civil Engineers, Journal of the Hydraulics Division
IS - 12
M1 - 04020082
ER -