DETERMINING THE ADEQUATE CREST HEIGHT OF SUPPRESSED RECTANGULAR BROAD CRESTED WEIRS UNDER SUB- CRITICAL FLOW CONDITIONS

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9 Issue 7 July 2018 pp Article ID: IJCIET_09_07_071 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed DETERMINING THE ADEQUATE CREST HEIGHT OF SUPPRESSED RECTANGULAR BROAD CRESTED WEIRS UNDER SUB- CRITICAL FLOW CONDITIONS Hayder Mohammed Jasim Civil Dept. Faculty of Engineering Kufa University Iraq Dr. Fadhel Abdulabbas Hassan Structures and water resources Dept. Faculty of Engineering Kufa University Iraq Tagreed Hameed Khlif Civil Dept. Faculty of Engineering Kufa University Iraq ABSTRACT In this research an experimental work was conducted on models of broad crested weirs with different height of crest and different flow conditions in sub critical zone to derive an equation to calculate the adequate height of a broad crested weir as a function of flow parameters such as initial depth sequent depth critical depth and Froude number due to the hydraulic jump will be generated downstream the weir. Five laboratory models were used in the experiments with crest heights of 30 cm 35 cm 40 cm 45 cm 50 cm and 55 cm. Each model will examined under different flow values (37 l/s 31 l/s 26 l/s 11 l/s and 6 l/s.). All experiments were conducted in a laboratory flume with dimensions of (1 m * 1.15 m) in cross section and 18 m length. The flow conditions and geometric parameters of laboratory models were rearranged as a non-dimensional parameters using Л theorem. The values of each Л will be scheduled and analyzed by the software of SPSS -21 to derive an empirical formula to calculate the non-dimensional height of crest. The value of the coefficient of determination (R 2 ) resulted from the non-linear regression of data to derive the nondimensional formula was very high. Key words: Broad Crested weir Sub- Critical Flow Suppressed Weir Crest Height. Cite this Article: Hayder Mohammed Jasim Dr. Fadhel Abdulabbas Hassan and Tagreed Hameed Khlif Determining The Adequate Crest Height of Suppressed Rectangular Broad Crested Weirs Under Sub-Critical Flow Conditions International Journal of Civil Engineering and Technology 9(7) 2018 pp editor@iaeme.com

2 Hayder Mohammed Jasim Dr. Fadhel Abdulabbas Hassan and Tagreed Hameed Khlif 1. INTRODUCTION A broad crested weir is the simplest hydraulic structure in which discharge in canals can be measured. It is usually an independent structure built in across the rivers or accompanying to a large hydraulic structure. Depending on the width of crest weirs may be classified in to two types which are sharp and broad. Number of researchers have studied flow over the crest of broad crested weirs. Gonzalez A. et al. (2007) [3] conducted experiments on a full scale of a broad crested weir to measure velocity profile and pressures due to flow over the crest of weir. The results showed that the design of overhanging crest effect on the field of flow while the upstream end of the weir have a rapid flow distribution during the experiments. Also the research showed that the vertical structures of a large scale may be observed towards the weir in the upstream side and this may be lead to negative impact on the flow pattern over the weir. Haun et al. (2011) [4] introduced two model of flow using two codes of computational fluid dynamics which are SSIIM 2 and 3D Flow to describe the flow over a trapezoidal broad crested weir. When the results have been compared with the results obtained from a laboratory test using different discharges the deviation between the computed and observed water level at upstream was between 1 % - 3.5%. While the difference between the results from the two models CFD was between 1 to 1.5 %. Hoseini S. (2014) [5] and Jan D. et al. (2009) [6] introduced a laboratory experiments to derive an equation to calculate the discharge coefficient and non dimensional discharge for a broad crested weir with different geometric and hydraulic parameters. The results of experimental work showed that the parameters of Froude number and (h1/l) having more effect on the coefficient of discharge. The comparison between calculated value of Cd or Q from derived equation and the others obtained from experimental work pointed out a very big match. Maghrebi et al. (2012) [7] formulate a 3 dimensional model using the software of Flow 3D as a simulation to the flow over the rectangular broad crested weir for a real case study of Gharnave check dam in Iran. Also the model contains a design for USBR stilling basin to dissipate the excess energy of flow by proposing two different types of basins. While Mohammadpour R. et al. (2013) [8] developed a 3- dimensional model as a simulation to the flow around gabion weirs under free surface conditions of water. The volume of fluid method with reconstruction scheme of geometric was applied to solve the complex conditions of free surface flow. Ramamurthy A. et al. (1988) [10] studied the flow characteristics over a square edged roundnosed of rectangular broad crested weirs. The study concluded the free flow and submerged flow conditions. Also Salmasi et al. (2012) [11] conducted number of experiments to investigate the effect of multi geometric parameters such as lower width of crest and step height for fifteen model of broad crested weirs under different flow conditions when the cross section is compound rectangular. Sarker M. A. et al. (2004) [12] introduced a laboratory study for the free surface profile over a rectangular broad crested weir. The results of the tests were compared with another set of results obtained from commercial software. For comparison purposes an excellent match between experimental and theoretical results when measuring the upstream water depth and the rapidly varied flow profile over the crest. 2. DIMENSIONAL ANALYSIS For the group of parameters that effect on selecting the suitable height of crest under different operation condition of flow a dimensional analysis for these variables could be done using Buckingham s π-theorem which is used to develop a dimensionless formula describe the editor@iaeme.com

3 Determining The Adequate Crest Height of Suppressed Rectangular Broad Crested Weirs Under Sub- Critical Flow Conditions relation between crest height (p) and other flow condition such as depth of water upstream the broad crested weir (yu) critical water depth over the crest of weir (yc) depth of water downstream the broad crested weir (yd) actual discharge passing through the flume (Qact) and coefficient of discharge (Cd). According to π-theorem the repeated variables is the following: ρ: Mass density of water (kg/m3) g: Gravitational acceleration (m/s2) and yd: depth of water downstream the broad crested weir (m) The general form of the formula can be as follow: P = f (ρ g Qact yu yc yd Cd) (1) After rearrangement according to Buckingham's theorem the dimensionless formula is: = f (. C d) (2) In which the parameter. is Froude number then equation (2) may be expressed as: = f (F C d) (3) Where Q act: Actual discharge passing through the flume (m 3 /s) : non dimensional height of crest F r : Froude Number : non dimensional critical depth of water over the crest : non dimensional depth of water upstream the broad crested weir C d : Coefficient of discharge 3. CALCULATION OF COEFFICIENT OF DISCHARGE Coefficient of discharge for suppressed rectangular broad crested weir is calculated from the following equation [1]: C d = (4) Where b : width of the crest (m) H: Total Energy (m) which is equal to: H = (upstream water level (yu) -crest level) + : Approach velocity head (m) and this value may be neglected because it is very small. 4. EXPERIMENTAL WORK All the experiments was carried out using a laboratory flume rectangular in the cross section which was constructed by the researcher as shown in figure 1. The flume dimensions is (18 m long * 1 m wide * 1.15 m deep) [9]. The laboratory models are installed at a distance of 7 m editor@iaeme.com

4 Hayder Mohammed Jasim Dr. Fadhel Abdulabbas Hassan and Tagreed Hameed Khlif from the gate of the head basin. The calibration of the flume was conducted using a standard weir (sharp crested weir with 90o V notch) according to the specification of USBR. As shown in figure 2 six models were used in the experimental work to derive the relation between non dimensional crest height ( ) and other hydraulic conditions (F Cd). The dimensions for all models are fixed in the value of (L) which is equal to 40 cm while the value of (P) varied from model to another which is equal to (30 cm 35 cm 40 cm 45 cm 50 cm and 55 cm) for the five models respectively. Each model was examined under different flow conditions for five values of actual discharges (37 l/s 31 l/s 26 l/s 11 l/s and 6 l/s.) editor@iaeme.com

5 Determining The Adequate Crest Height of Suppressed Rectangular Broad Crested Weirs Under Sub- Critical Flow Conditions All dimensions of models meet the specifications and limitation of ASTM International Designations [2]: 1. H 0.06 m H/L H/P < P 0.15 m 5. B 0.3 m or H or L/5 6. L 1.75 H 5. RESULTS AND DISCUSSIONS 5.1. The relation between (P/yd) and (Fr) The dominant factor that effect on the flow in open channel is Froude number. Regardless the value of Froude number and whether the hydraulic jump occurs or not the value of Froude number must be calculated and takes into account when developing any empirical formula describe the flow in open channel. Figure 3 shows a positive relationship between the height of crest (P) and the value of Froude Number (Fr). For the same value of discharge the value of (Fr) increased when the value of (P) increased because of when water flows from a high crest the flow velocity increases at downstream of the weir and thus the value of Froude number increases. The value of (Fr) is when (P) equal to 55 cm while (Fr) equal to for (P) equal to 30 cm for the same value of discharge which is equal to 37 l/s editor@iaeme.com

6 Hayder Mohammed Jasim Dr. Fadhel Abdulabbas Hassan and Tagreed Hameed Khlif Figure 3 The Relation between (P/y d) and (Fr) for the Six Models 5.2. The relation between (P/yd) and (yc / yd) Figure 4 shows an inverse relationship between the height of crest (P) and the critical depth of water (yc). The greater value of the critical depth over the crest was 16 cm and it is recorded when the discharge equal to 37 l/s and for P equal to 30 cm. Laboratory experiments also recorded the lowest critical depth of 11 cm for the same value of discharge and for P value equal to 55 cm. While the relationship is positive when reducing the value of the discharge where the value of the critical depth decreased by reducing the value of Q for the same model (i.e. P value is constant). Figure 4 The Relation between (P/y d) and (y c/y d) for the Six Models 5.3. The relation between (P/yd) and (yu / yd) When the height of weir increased the amount of retained water increased so the height of water column increased also. This fact is very clear in figure (5) which show the relationship between the height of crest (P) and depth of water at upstream (yu). The greater value of (yu) was 67.4 cm and it is recorded when the discharge equal to 37 l/s and for P equal to 55 cm editor@iaeme.com

7 Determining The Adequate Crest Height of Suppressed Rectangular Broad Crested Weirs Under Sub- Critical Flow Conditions The lower value of (yu) recorded was 52 cm for the same value of discharge and for P value equal to 30 cm. The relationship remains positive for the same model when reducing the value of the discharge where the value of (yu) decreased by reducing the value of Q. Figure 5 The Relation between (P/y d) and (y u/y d) for the Six Models 5.4. The relation between (P/yu) and (Cd) Figure 6 shows a positive relationship between the height of crest (P) and the value of coefficient of discharge (Cd). The value of coefficient of discharge (Cd) for model no. 6 (for five values of discharges and P = 55 cm) was While the value of (Cd) for the first model which has the lower crest (P = 30 cm) was Also in the same model the value of (Cd) increased when the value of actual discharge decreased. Figure 6 The Relation between (P/y d) and (C d) for the Six Models 6. DERIVATION OF A NEW FORMULA Using the software of SPSS v21 and 80% of the experimental data the following non dimensional formula was derived relates between the non dimensional height of crest (P/yd) and other parameters resulted from dimensional analysis (F Cd): editor@iaeme.com

8 Hayder Mohammed Jasim Dr. Fadhel Abdulabbas Hassan and Tagreed Hameed Khlif # $ % = (.)** +.)( -. +( $ 2 $ % $ 6 $ % 3+( % (5) Where the coefficient of determination (R 2 ) equal to CHECK THE ACCURACY OF THE FORMULA To check the accuracy of equation (5) the rest of the experimental data which are not used in the non linear regression to derive equation (5) will be applied in the new formula to compare the results from equation and the other resulted from experimental work as illustrated in table 1: Table 1 A Comparison between experimental results and equation results for the value of (P/y d) (P/y d) from Experimental Work (P/y d) from Equation (5) Percentage of Difference % CONCLUSIONS 1. The difference percentage values of (P) obtained from experimental work and calculated from equation (5) ranged between 1.31% to 8.41%. This confirms that there is a large matching between two sets of values. 2. The results showed that there is a positive relation between Froude number and (P) and this relation governed with a limited values of flow (Qact). 3. There is a negative relation between (P) and (yc) for a fixed value of (Qact) but when the value of (Qact) decreased for a fixed value of (P) the value of (yc) increased also. 4. The relationship between (yu) and (P) remains positive whether within the same model or between the six models. REFERENCES [1] Al-Hashimi S. et al. " Flow over Broad Crested Weirs: Comparison of 2D and 3D Models" Journal of Civil Engineering and Architecture Vol p.p [2] ASTM International Designation "Standard Guide for Selection of Weirs and Flumes for Open-Channel Flow Measurement of Water" United States [3] Gonzalez C A & Chanson H "Experimental measurements of velocity and pressure distributions on a large broad-crested weir" Flow Measurement and Instrumentation p.p [4] Haun S. et al. "Numerical Modeling of Flow over Trapezoidal Broad Crested Weir" Engineering Application of Computational Fluid Mechanics Vol. 5 No p.p [5] Hoseini S. "Experimental investigation of flow over a triangular broad-crested weir" ISH Journal of Hydraulic Engineering Vol. 20 Issue p.p [6] Jan C D Chang C J & Kuo F H "Experiments on discharge equations of compound broadcrested weirs" Journal of Irrigation and Drainage Engineering 135(4) 2009 p.p editor@iaeme.com

9 Determining The Adequate Crest Height of Suppressed Rectangular Broad Crested Weirs Under Sub- Critical Flow Conditions [7] Maghrebi M. et al. " Numerical Simulation of Flow Over Rectangular Broad Crested Weir (Real case study)" The First International Conference on Dams and Hydropower Tehran Iran [8] Mohammadpour R. et al. "Numerical Modeling of 3-D Flow on Porous Broad Crested Weirs" Applied Mathematical Modelling Vol p.p [9] Omran H. et al. "The Effect of Hydraulic and Geometric Parameters on the Scouring Downstream Combined Structures" International Journal of Trend in Research and Development Volume 3(6) 2016 ISSN: [10] Ramamurthy A. S. Tim U. S. and Rao M. J. Characteristics of Square-Edged and Round-Nosed Broad-Crested Weirs. Journal of Irrigation and Drainage Engineering p.p [11] Salmasi F. et al. "Discharge Relations for Rectangular Broad-Crested Weirs" Journal of Agricultural Sciences Vol p.p [12] Sarker M. A. and Rhodes D. G. Calculation of Free-Surface Profile over a Rectangular Broad-Crested Weir. Flow Measurement and Instrumentation 2004 Volume 15 (4): editor@iaeme.com