Flow resistance corrections for physical models using unit flowrates
Date
2024
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Abstract
Flow resistance is an essential aspect of evaluating flow behavior in open-channel hydraulic models. Flow resistance in open channels is commonly characterized by Manning's resistance equation, where a value of Manning's roughness coefficient n, indicates the magnitude of flow resistance. Physical hydraulic models are one method to estimate Manning's n values for prototype channel reaches. A physical hydraulic model evaluates prototype channel characteristics at the model scale. The scale for a given physical model may be characterized by length-scale factor, given by the relationship of prototype to model geometry. Models that have a large length-scale factor are known to introduce errors associated with instrumentation, measurement, and scale effects, therefore minimization of the length-scale factor is an important consideration in the development of hydraulic models. Evaluating physical models using a scaled unit flowrate provides a method by which the length-scale factor may be minimized. In this way, a scaled design discharge per unit width of channel is applied to a channel that is less wide than the prototype design. Using this approach greatly improves the ability of laboratories to utilize available facilities, without being constrained by prototype design width, which can otherwise be a driving factor increasing the length-scale factor for a given model. This thesis documents the construction and analysis of two physical models of a proposed rectangular canal along Rio Puerto Nuevo in San Juan, Puerto Rico. One model used a scaled unit flowrate and a reduced channel width at a lesser length-scale factor, and the other model accommodated the total scaled design flowrate and design channel width at a larger-scale factor. Tests were conducted for three sidewall conditions to identify the impact associated with applying a unit flowrate physical modeling approach for models with different Manning's n values specific to the sidewalls. The unit flowrate approach was found to result in larger estimates of flow depth and composite Manning's n compared to the model that accommodated the full prototype channel width. Insights regarding the variability of Manning's n as a function of channel width for each sidewall condition were identified by comparing results from the two models. A correction method was proposed for improving estimates of Manning's n derived from scaled unit flowrate models. Correction factors were identified as a function of two dimensionless parameters, relative prototype channel width (defined as the ratio of the width evaluated using a unit flowrate model to the design width of the channel), and relative flow resistance exerted by the individual boundary elements as determined from the unit flow rate model (defined as the ratio of Manning's n values between the sidewall and channel bed boundary elements). Findings indicate that it becomes increasingly important to apply correction factors to flow resistance estimates on unit flowrate models when wall boundary elements exert a larger contribution to flow resistance than that of the channel bed (large relative roughness), and when the scaled unit flowrate approach results in a prototype channel width that is significantly smaller than the proposed design channel width (small relative channel width). Correction factors were developed for a range of relative channel width values from approximately 0.4 to 1.0, and a range of relative roughness values from approximately 0.5 to 3.0. Future physical models using unit flowrates with relative channel widths and relative flow resistance within the range evaluated may use the presented correction methods to improve estimates of flow resistance.
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Subject
flow resistance
physical models
unit flowrate
Manning's n
correction factors
unit discharge