نوع مقاله : مقاله پژوهشی

نویسندگان

• رضا فرزان پور ¹
• صلاح کوچک زاده ²
• شبنم مغیث پور ³

¹ گروه علوم و مهندسی آب، پردیس بین الملل کیش، دانشگاه تهران

² گروه مهندسی آبیاری و آبادانی، دانشکدگان کشاورزی و منابع طبیعی، دانشگاه تهران، کرج، ایران.

³ دکتری سازه های آبی، دانشجوی سابق دکتری گروه مهندسی آبیاری و آبادانی دانشگاه تهران

چکیده

تخمین درست ضریب زبری مانینگ برای طراحی کانال‌های روباز، روندیابی سیلاب و مهندسی رودخانه ضروری است. با این حال، روش‌های متداول آزمایشگاهی برای تعیین این ضریب، مبتنی بر برقراری جریان شبه یکنواخت هستند که وقت‌گیر و همراه با عدم‌قطعیت بالاست. در اینجا یک رویکرد جایگزین مبتنی بر جریان متغیّر تدریجی برای تخمین ضریب مانینگ در شرایط آزمایشگاهی ارائه شده است. آزمایش‌ها در فلوم مستطیلی به طول ۱۲ متر با استفاده از سه زبری بستر شامل آهن گالوانیزه، کف‌پوش‌های مشبک از جنس پلی‌وینیل کلراید (PVC) با پایه‌های کوتاه و مشبک متراکم با پایه‌های بلند به­اجرا در آمدند. شیب‌های طولی مختلف و با 9 دبی (۱۰ تا ۹۰ لیتر بر ثانیه با گام‌های ده لیتر برثانیه) آزمون شدند. نیمرخ‌های سطح آب با استفاده از یک شبکه متراکم پیزومتری و سامانۀ خودکار حسگرهای فشار اندازه‌گیری شدند. به‌جای ایجاد جریان شبه‌یکنواخت، با باز کردن کامل دریچه پایین‌دست، نیمرخ‌های M2 برقرار شد و ضریب زبری مانینگ با کمینه‌سازی مجموع مربعات اختلاف بین نیمرخ‌های مشاهده‌شده و محاسبه‌شده از معادله جریان متغیّر تدریجی تعیین شد. نتایج تحقیق نشان داد که تأثیر دبی بر ضریب زبری به‌طور کلی جزئی و نامنظم است و تأثیر شیب نیز در محدودۀ آزمون‌شده در درجه دوم اهمیت قرار دارد. عدد رینولدز برشی نشان داد که هر دو بستر مشبک در رژیم کاملاً متلاطم و زبر قرار دارند در حالی‌که بستر گالوانیزه در ناحیۀ انتقالی  است. تحلیل حساسیت نشان داد که تعدیل عمق جریان تا ۱ سانتی‌متر برای لحاظ کردن ضخامت فیزیکی پوشش‌ها تغییری کمتر از ۱ درصد در اندازه زبری معادل محاسبه شده ایجاد می‌کند که گویای استواری نتایج است. روش پیشنهادی مبتنی بر جریان متغیّر تدریجی، جایگزینی عملی، تکرارپذیر و با عدم‌قطعیت کمتر برای تخمین ضرایب زبری در فلوم‌های آزمایشگاهی فراهم می‌آورد و کاربرد مستقیمی در مجاری طبیعی دارد که جریان متغیّر تدریجی در آنها قاعده است نه استثنا.

کلیدواژه‌ها

• ارتفاع زبری معادل
• شیب بستر
• ضریب زبری مانینگ
• عدد رینولدز برشی
• کانالهای روباز

موضوعات

• هیدرولیک

عنوان مقاله [English]

Estimation of Open Channel Flow Resistance Coefficient Under the Effect of Slope and Discharge Variation Using Gradually Varied Flow

نویسندگان [English]

• Reza Farzanpour ¹
• Salah Kouchakzadeh ²
• Shabnam Moghispour ³

¹ Ph.D. candidate, Kish International Campus, University of Tehran.

² Professor, Irrigation and Reclamation Engrg. Dept., University college of Agriculture and Natural Resources, University of Tehran, Iran.

³ Ph.D. Hydraulic structure, formerly graduate student, Irrigation and Reclamation Engrg. Dept., University college of Agriculture and Natural Resources, University of Tehran, P.O.

چکیده [English]

Extended Abstract
Introduction
Historically, the determination of Manning's roughness coefficient, n, has relied on two approaches: (1) field measurements, and (2) laboratory experiments in flumes where quasi-uniform flow is artificially established. While field data are most realistic, they suffer from uncontrolled variables and high costs. Laboratory studies offer controlled conditions but face a fundamental challenge: establishing truly uniform flow in a flume requires a long channel length, precise slope adjustment, and a downstream control that balances friction losses—a condition that is rarely achieved in practice
Studies by Tracy and Lester (1961) and Kazemipour and Apelt (1979, 1982, 1999) demonstrated that even in relatively long flumes, achieving true uniform flow is difficult and time-consuming. Moreover, in natural rivers, uniform flow is the exception rather than the rule; gradually varied flow dominates due to changes in cross-section, slope, and roughness along the channel.
This study proposes a paradigm shift: instead of forcing uniform flow in the laboratory—which introduces uncertainty and limits repeatability— the GVF was used as the basis for estimating Manning's coefficient. The M2 profile provides a well-defined water-surface profile that can be accurately measured and compared with theoretical GVF solutions. By optimizing n to minimize the discrepancy between observed and computed profiles, we obtain a robust estimate of the roughness coefficient that is both physically meaningful and practically reproducible.
The primary objectives of this research were: To develop and validate a GVF-based methodology for estimating Manning's n in a laboratory flume; To investigate the effects of three different bed roughness types on n; to quantify the influence of longitudinal slope and discharge on n; to compare the experimental results with theoretical resistance laws and assess the flow regime (hydraulically smooth, transitional, or rough); to perform a sensitivity analysis regarding the choice of reference depth for roughness-height estimation.
Methodology
Experimental Setup
Experiments were conducted in a rectangular flume located at the Central Water Research Laboratory of the University of Tehran. The flume has a length of 12 m, a width of 0.8 m, and a depth of 0.6 m. The flume is mounted on an adjustable platform capable of setting longitudinal slopes. Water-surface profiles were measured using data-acquisition system designed for the current research. Three bed materials, 9 longitudinal slopes, and 9 discharges were tested.
 Experimental Procedure and Data Analysis
For each bed roughness the desired slope was set, and the flow was established. The downstream gate was fully opened to create a free overfall, generating an M2 gradually varied profile. After steady-state conditions were reached, the water surface elevations along the flume were recorded.
Manning's n was determined by solving the standard GVF equation for a prismatic channel. For each experimental profile, the value of n was optimized to find the best match between the observed and the computed profiles. The equivalent roughness height, k_s, was then calculated.
Results and Discussion
The optimized Manning's n values for all 81 runs are summarized in Tables 1–3 of the main Contrary to some previous studies (e.g., Merry, 2017; Yilmaz et al., 2023), which reported a decreasing trend of n with increasing discharge, the results did not show a systematic or monotonic relationship. For most roughness–slope combinations, n remained approximately consistent across the discharge range. Small fluctuations (typically ±0.002) were observed but did not follow a consistent pattern. This suggests that within the tested range of relative submergence, the effect of discharge on bulk resistance is secondary to the geometric roughness characteristics. Similarly, slope variations produced only minor changes in n.
Computed shear Reynolds numbers ( ) revealed that both bed materials of C2 and C3 operated in the fully rough turbulent regime ( ), confirming that viscous effects were negligible. In contrast, the galvanized bed (C1) fell within the transitional regime.
Because the piezometers were connected to the flume floor (i.e., below the installed mesh covers), measured depths included the physical thickness of the roughness elements. To assess whether this introduced systematic bias, the reference depth was artificially reduced by 0.5 cm, 1.0 cm, and 1.5 cm, and the entire optimization was repeated. The resulting changes in k_s were consistently less than 1%, and the flow regime classification remained unchanged. This demonstrates that the methodology is robust and insensitive to minor uncertainties in vertical datum selection.
Conclusions
This study validates a novel experimental approach for estimating Manning's n using gradually varied flow (M2 profiles), which offers a practical, repeatable, and lower‑uncertainty alternative to conventional uniform‑flow methods in laboratory flumes. By leveraging gradually varied flow—which prevails in natural channels—this approach bridges the gap between laboratory studies and field applications, offering a physically relevant framework for river engineering and flood modeling.
Keywords: Equivalent roughness, Longitudinal slope, Manning's roughness coefficient, Open Channels, Shear Reynolds number
 Conflict of Interest
       The authors declare that they have no conflict of interest. All authors have read and approved the final manuscript.
 Funding
The corresponding author conducted this study as an extension of the research project entitled “Experimental Investigation of the Effects of Hydraulic Crossing Structure Geometry on the Trapping of Large Woody Debris and the Aggravation of Flood Hazards,” carried out at the Soil Conservation and Watershed Management Research Institute. The present research was undertaken to develop practical measures for reducing flood risks associated with woody debris accumulation at bridges. No financial support was received from any public, commercial, or non-profit organization for conducting, writing, or publishing this study.
 Data Availability Statements
       All relevant data and results supporting the findings of this study are presented within the article. The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.
 Author Contribution
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by all authors. The first draft of the manuscript was written by R.F. and all authors commented on previous versions of the manuscript (R.F., S.K., and S.M.). The final revisions have been applied by S.K. and Moreover, all authors have read and approved the final manuscript.
All authors contributed equally to the conceptualization of the article and writing of the original and subsequent drafts.
 Acknowledgement
The vice dean for research affair of the University of Tehran is Acknowledged for providing the research facility of the Central Lab for Water Research

کلیدواژه‌ها [English]

• Equivalent roughness
• Longitudinal slope
• Manning's roughness coefficient
• Open Channels
• Shear Reynolds number