Experimental and numerical research on trapezoidal sharp-crested side weirs

Author’s Accepted Manuscript Experimental and numerical research on trapezoidal sharp-crested side weirs Yingying Wang, Wene Wang, Xiaotao Hu, Fulai Liu www.elsevier.com/locate/flowmeasinst

PII: DOI: Reference:

S0955-5986(17)30022-5 https://doi.org/10.1016/j.flowmeasinst.2018.10.005 JFMI1470

To appear in: Flow Measurement and Instrumentation Received date: 10 February 2017 Revised date: 30 June 2018 Accepted date: 7 October 2018 Cite this article as: Yingying Wang, Wene Wang, Xiaotao Hu and Fulai Liu, Experimental and numerical research on trapezoidal sharp-crested side weirs, Flow Measurement and Instrumentation, https://doi.org/10.1016/j.flowmeasinst.2018.10.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Experimental and numerical research on trapezoidal sharp-crested side weirs Yingying Wanga,b, Wene Wanga,*, Xiaotao Hua, Fulai Liua a Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, Yangling, Shaanxi, PR China b Fuzhou Institute of technology, Fuzhou, Fujian, PR China *Corresponding author. E-mail address: [email protected] (W. Wang)

Abstract: In this paper, the hydraulic characteristics of side weirs, such as Froude number distribution, water profiles, velocity distribution and discharge coefficient were investigated. Experiments and simulations with FLOW-3D software were performed on side weirs with four different crest angles under different conditions. The results showed that the simulated and the observed water depths were similar with a relative error below 5.63%. The relationships between discharge coefficient and its parameters were studied based on dimensional analysis, and regression models were established under different working conditions with a maximum relative error of 9.25%, which met the common requirements of flow measurement in irrigation districts. The hydraulic characteristics of trapezoidal sharp-crested side weirs was preliminarily characterized, which provided useful information on the performance of flow measurement devices placed in water inlet of field. Keywords: Side weir; Simulation; Velocity; Discharge coefficient

List of notations Symbol Description Q discharge over side weir (m3/s) b side weir length (m) Pu side weir height in upper end (m) B channel width (m) v mean velocity (m/s) h1 water depth upstream side weir in the main channel (m) μ dynamic viscosity of fluid (N s/m2) σ surface tension (N/m) g gravitational acceleration (m/s2) ρ fluid density (kg/m3) s bed slope of the channel θ side weir crest angle m discharge coefficient H total water head over side weir (m) Fr1 Froude number upstream side weir in the main channel t time (s) i,j i=1,2,3; j=1,2,3 ui , uj u1,u2,u3 represent average flow velocity components in Cartesian coordinates x,y and z, respectively(m/s) Si body force, S1=0, S2=0, S3= -ρg (N)  turbulence dissipation rate (kg m2/s2) p pressure (Pa) xi,xj x1,x2 and x3 represent Cartesian coordinates x,y and z, respectively 

*

1

k turbulence kinetic energy (m2/s2) μeff effective hydrodynamic viscous coefficient, μeff=μ+μt, μt=ρCμk2/ε, Cμ=0.0845(N s/m2) Gk generation item of turbulence kinetic energy k due to gradient of the average flow velocity,

 u u  u Gk  t  i  j  i  x   j xi  x j αk, αε

αk=αε=1.39

C1* ,C2ε C1*  C1 

k 1/2  1  / 0   ,C1ε=1.42,   2 E  E   ij ij 1   3

1  u u  Eij   i  j  , 0 =4.377,β=0.012, C2  1.68 2  x j xi 

1. Introduction Along with global climate change, water shortage has become one of the most important restriction factors for social and economic development. Therefore, it is critically important to achieve sustainable utilization of water resources; particularly efficient water management in agriculture as it accounts for more than 70% freshwater. In a series of research works, Valipour studied the change of irrigation-equipped areas as share of cultivated areas [1] and stressed the importance of water management in irrigation areas. The author presented the devices and approaches to assess and improve irrigation efficiency, such as cutback and surge irrigation [2], surface water supply index [3], an evolution of SWDC and WinSRFR models [4], water lifting devices [5] and so on. In addition, the experience on irrigation management was also discussed [6]. In recent years, in order to save water and improve irrigation efficiency, water-measuring devices are often used in irrigation water management. A side weir, as a flow diversion device, has been frequently used in irrigation and hydraulic engineering. It can be connected directly to channels without changing channel cross section structure. Its practice in flow measurement has receiving much attention owing to its shape simplicity and high accuracy. Number of studies on side weirs dealt mainly with theoretical analysis of side weir discharge coefficient. In 1934, De Marchi [7] first proposed the concept of constant specific energy, which had often been cited in studying flow characteristics of side weirs. Chen [8] concluded that theorem on the kinetic energy was more suitable for theoretical analysis of side weirs. Eminem [9] derived discharge coefficient formula for trapezoidal side weirs in trapezoidal channels. Based on aforementioned studies, more and more approaches for estimating discharge capacity of side weirs were developed in the later 20th century. Muslu [10] developed a numerical model to analyze discharge and water profiles. And the numerical model was successfully validated through experimental data. Cosar et al [11] performed experiments on the triangular side weir both in the straight channel and the curved channel, and found that discharge coefficient in the straight channel was bigger than that in the curved channel. Fiaz [12] investigated the variation of discharge coefficient along broad-crested inclined side weirs in relation to height, width and slope of side weirs through a comprehensive laboratory study. Emin [13] found the discharge coefficient of labyrinth side weirs was significantly higher compared to that of classical side weirs and it was 1.5-4.5 times higher than rectangular side weirs. Other investigators such as those by Omer [14], Emin [15] and Bagheri [16] conducted experiments on rectangular side weirs, and analyzed relationship between discharge coefficient and its influence factors. In recent years, with the development and implementation of computational fluid dynamics, numerical simulation technology is used to 2

simulate the free surface flow of water-measuring devices in canals. Aydin et al [17] conducted experiments and simulations on the triangle labyrinth side weir and comparison between experimental and simulated results yielded a solid agreement between results from two methods. Aydin and Emiroglu et al [18] studied discharge coefficient, Froude number, side weir crest angles, etc. Aydin et al [19] made self-priming siphon that serves as side weir and characterized the hydraulic properties inside the siphon. A review of literature indicates that sharp-crested side weirs have been studied experimentally and discharge formulas have been developed. However, the experimental works are labor intensive and the experimental results are influenced by model size, measurement accuracy, etc. Moreover, discharge formulas obtained by researchers are either contained Froude number or complex, thus irrigation managers could not get discharge over side weirs easily. In the present study, the trapezoidal sharp-crested side weirs were evaluated in combination with experimental measurements and simulations with FLOW-3D software, and discharge formulas with simple forms were developed. 2. Theory Emin [15], Aydin [20] and Bagheri [21] have derived discharge coefficient by dimensional analysis. Discharge over sharp-crested side weirs is a function of different dominant physical and geometrical quantities, as follows: （1） Q  f (b, Pu , B, v, h1 , g ,  ,  ,  , s, ) In experiments where the upstream weir head y1>30 mm, effects of surface tension on discharge were found to be minor [22]. The viscosity effect was far less than the gravity effect in a turbulent flow. Hence μ [23] and σ [24] were excluded from the analysis. In addition，the side weir length, the channel width, the bed slope of the channel and the water density were all constant, so discharge formula can be simplified as:

Q  f1 ( Pu , v, h1 , g , )

（2）

Based on dimensional analysis, Q is given by:

Q

P h1 v F1 ( u , , )b 2 gh11.5 h1 gh1 2b

（3）

In a flow over a frontal weir, discharge over a side weir is proportional to H1.5 (H=y1+v2/2g), so Eq.(3) can be transformed as:

Q

P h1 v F1 ( u , , )b 2 g H 1.5 h1 gh1 2b

（4）

Consequently, the discharge formula of trapezoidal sharp-crested side weir is defined as:

Q

P 2 mb 2 g H 1.5 ，in which m  F1 ( u , Fr1 , ) h1 3

（5）

3. Experimental setup The experimental setup contained a pumping station, an electromagnetic flow meter, a regulating valve, a stabilization pond, a side weir and backwater drainage. A schematic plan of the experimental setup was given in Fig. 1. The main channel was 12.24 m long, 0.47 m wide and 0.6 m deep. Trapezoidal sharp-crested side weirs were designed with four different crest angles. Side weirs were placed at the side of the main channel. It was known from experience that flow capacity of the ditch in irrigation areas ranged from approximately 10L/s to 40L/s [25]. The actual discharges were measured by an electromagnetic flow meter with a precision of ±3‰. Flow depths at the main channel centerline were recorded by point gauge, with an accuracy of ±0.1 mm. To study water profiles near the side weir in the main channel, corresponding cross-sections were established and experimental data was recorded. Measuring points located near the side weir, in the main channel centerline and away from the side weir, and were denoted respectively as ①，②and ③(Fig. 2).

3

Fig.1. Plan sketch of experimental system.

4. Numerical simulation 4.1 Governing equations and turbulence model Numerical simulations were performed with the CFD (Computational Fluid Dynamics) software FLOW-3D. The continuity and Navier-Stokes equations for incompressible, viscous flow based on Cartesian coordinates are given by Eqs. (6) and (7):

    ui   0 t xi

(6)

   ui     ui u j    ui  p    Si   t x j x j  x j  xi

(7)

Since the flow near the side weir is complex, truVOF method was used to track the change of free surface. The RNG k-ε three-dimensional turbulence model was employed (Eq.(8) and Eq.(9)):

   k     kui    k     k eff   Gk   t xi x j  x j         ui     t xi x j

   C1* 2    G  C    eff  k 2 x j  k k 

(8)

(9)

4.2 Mesh generation and boundary conditions According to the actual size of the side weir and the experimental setup, three-dimensional geometrical models were developed using the software AutoCAD. To simplify iterative calculation and reduce the simulated time, the length of the main channel was reduced to 7 m. Structured block grid was used and the size of a unit grid was set at 0.02 m in length, 0.02 m in width and 0.02 m in height. The total number of grids is about 40 millions. The boundary conditions of the mathematic model are shown as Fig. 2. The water inlet boundary was a specified volumetric flow rate set in the channel inlet with an auto-adjusted fluid height. An outflow-outlet condition was positioned at the end of the side channel. Moreover, a symmetry boundary condition was set in the air inlet at the top of the model, which represented that no fluid flows through the boundary. The bottom of the channel and the side walls were set as a wall boundary condition. 4

Fig.2. Physics model and boundary conditions, schematic sketch of parameters of side weir and measuring points.

5. Results and discussion 5.1 Flow pattern Froude number is a dimensionless parameter used to discriminate flow pattern. Froude number distributions in the whole flow field under different conditions were analyzed. From Fig. 3 it can be seen that Froude number in the main channel was less than 1, which indicated flow pattern in the main channel was subcritical flow. As water kept on flowing over side weir, Froude number increased gradually, and the greatest value of Froude number appeared upstream of the side weir in the side channel. Flow pattern was then transformed from subcritical flow to supercritical flow. a b

Note：Discharge was 27.70L/s under free flow condition. Fig.3. Variation of Froude number of side weir. (a) Simulated flow pattern in the whole flow field, (b) Simulated flow pattern in side channel. 5

5.2 Water surface profiles Flow pattern can be described by analyzing water surface profiles qualitatively [26]. And water surface profiles were essential parameter for choosing water-measuring devices [8]. Fig. 4 displays the variation of water surface profiles near the side weir in the main channel. Zero-point of x-coordinate located in section Ⅴ. From Fig. 4, one could see that the water surface profiles were backwater curve. Flow fluctuated stronger near the side weir than that in the centerline of the main channel and the opposite side wall, indicating that the side weir entrance effect didn’t spread as far as the centerline of the main channel, but occurred only near the side weir crest, consistent with as the findings by Emiroglu et al.[15]. Fig. 5 shows the variation of water surface profiles under different crest angles of trapezoidal side weir. It was found that the flow depth increased with the reduction of side weir crest angles under the same discharge. The water surface level went down at the upstream end of the side weir (section Ⅰ~ section Ⅲ). As water was kept on flowing over the side weir, the water surface in front of the side weir (section Ⅲ~ section Ⅶ) rose and the gaining rate increased. When water flowed through the side weir, water surface rose slowly to a steady level. The water surface profiles near the side weir were illustrated in Fig. 6 (when discharge was 27.70L/s and side weir crest angle was 6°). The accuracy between the experimental and simulated values was 5.63% in maximum, indicating a satisfactory agreement between the experimental and simulated results.

Water depth/cm

24

Each side of main channel ①

②

26.5

③

θ= 0°

23 22

θ= 6°

21

20 Ⅰ Ⅱ Ⅲ Ⅵ Ⅶ Ⅷ Ⅸ Ⅳ Ⅴ 19 -44 -36 -28 -20 -12 -4 4 12 20 28 36 44

Side weir crest angles 9°

Water depth/cm

25

Distance from section Ⅴ/cm

6°

3°

0°

24.5

22.5 20.5

Ⅰ Ⅱ

Ⅲ

Ⅳ

Ⅴ

Ⅵ

Ⅶ

Ⅷ

Ⅸ

18.5

-44 -36 -28 -20 -12 -4 4 12 20 28 36 44 Distance from section Ⅴ/cm

Fig.4 Water surface profiles in the main channel of side weirs with different heights When Q=34.79L/s. Fig.5 Water surface profiles in the main channel of side weirs with different heights When Q=27.70L/s.

20 15

10 5

Simulated value Experimental value

25 20 15

10

c Simulated value Experimental value

30

Water depth/cm

Water depth/cm

25

b 30

Water depth/cm

a 30

25

Simulated value Experimental value

20 15

10

5

5 -46 -23 0 23 46 -46 -23 0 23 46 -46 -23 0 23 46 Distance from section Ⅴ/cm Distance Ⅴ/cm when discharge Fig.6 Flow profilesfrom in thesection main channel is 27.70L/s, side weir crest angle is 6°.Distance (a)Flowfrom depthsection of side Ⅴ/cm near side weir, (b) Flow depth of centerline in main channel, (c) Flow depth of opposite side in main channel

5.3 Distribution of velocity Velocity distribution near the side weir with a discharge of 27.70L/s and a side weir crest angle of 6° was presented in Fig. 7. As seen in Fig. 7, the flow velocity in the main channel was small. As water flowed over the side weir, the flow direction was deflected to the side weir and the deflection angle increased as water kept on flowing. However, the deflection angle in the section from the centerline to the opposite side in the main channel was almost unchanged, which showed again that the influence on flow from side weir was minor near the side weir. The backflow phenomenon occurred downstream of the side weir after water flowed through the side weir. The velocity turned into negative with velocity vector angle deflected. The maximum absolute value of velocity appeared upstream and downstream of the side weir. 6

Variation of velocity near the side weir was analyzed. Fig. 8 shows that the velocity value changed slightly in the part of 28 cm away from the side weir in the direction vertical to the flow direction. The cross-sectional velocity distribution presented a decreased trend from the middle to both sides. Maximum value of velocity located over the side weir.

Fig.7. Velocity distribution in main channel when discharge is 27.770L/s, side weir crest angle is 6°.

Fig.8. Development of cross-sectional velocity distributions near side weir.

5.4 Discharge coefficient formula Regression model is a mathematical model for quantitative analysis of statistical relations and it was used to calculate side weir discharge. It has been successfully used in many fields. Valipour has used regression models to obtain rainfall, evapotranspiration, etc [27-32]. Based on Valipour’s studies, the regression models of side weir discharge coefficient were obtained. Discharge coefficient was related to the ratio between the 7

side weir height and the flow depth, Froude number and the side weir crest angle. The relationships between the discharge coefficient and its influencing factors were analyzed, as shown in Fig. 9 and Fig. 10. The discharge coefficient tended to decrease as Froude number increased, and decrease even more as the side weir crest angle was bigger. This behavior was because that the water particles were forced by centrifugal inertial force besides gravity and under this two forces, lateral and vertical velocity existed in flow except longitudinal velocity. The effect of the secondary flow created by the lateral flow increased with side weir inclined angles, thus discharge angle and kinetic energy of flow over side weir increased along the side weir width. Fig. 10 shows the discharge coefficient tended to increase as the ratio of the side weir height to the flow depth increased. The gaining rate increased with the side weir inclined angle. 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

side weir crest angles

0.10

0.14

side weir crest angles 9° 6° 3° 0°

m

m

9° 6° 3° 0°

Fr1

0.18

0.22

0.5

0.6

P/h1

0.7

0.8

. Fig.9. Variation of coefficient of discharge with approaching Froude number Fig.10. Variation of coefficient of discharge with percentage of side weir height to approaching water depth above it.

The relationship of the discharge coefficient and the Froude number was highly significant with a R2 of 0.891 as shown in Eq. (10). The discharge coefficient was correlated well to the ratio of the side weir height to the flow depth with a R2 of 0.908 as shown in Eq. (11). The relationship of the discharge coefficient, Froude number and the ratio of the side weir height to the flow depth was also highly significant (R2=0.923) as shown in Eq. (12). All of the proposed discharge coefficient formulas were high in precision and with simple form. The measured discharge coefficient values were compared with those predicted with Eq. (12) and given in Fig. 11. In Fig. 11 we can see relative errors were limited to 10%, which met the accuracy demand of flow measurement in irrigated districts [25]. It has been difficult to measure and calculate Froude Number, so Eq. (11) was chosen as the computational formula when high precision is not necessary but within the error box. Eq. (12) was chosen as the computational formula when high precision is needed. m=1.233+4.932t anθ-4.319Fr1，R2=0.891 （10） 2 m=-0.645+2.510tanθ+2.042P/h1，R =0.908 （11） m=-4.897-3.017tanθ+6.548P/h1+10.236Fr1，R2=0.923 （12） For Eqs. (10), (11) and (12), the discharges ranged from 0.019 m3/s to 0.040 m3/s; the ratios of the side weir height to the flow depth ranged from 0.53 to 0.79; the side weir crested angles ranged from 0°to 9°. It should be pointed out that the sources of error in this study are mainly due to manual measurement, such as measurement of the fluid depth. To reduce this, multiple measurements of the same depth should be performed and the average value should be used as the actual depth.

8

1.6 1.4

Calculated m

1.2 1.0

Using Eq.(12) +10% 45°line -10%

0.8 0.6

0.4 0.2 Fig.11. Comparison of the measured discharge coefficient values with those calculated from Eq. (12).

0.0 6. Conclusions In the present study, experiments and study the1.6 0.0simulations 0.2 with 0.4FLOW-3D 0.6 software 0.8 were 1.0performed 1.2 to 1.4 hydraulic characteristics of the side weirs. The results of the numerical model Measured m agreed well with the experimental results related to the flow pattern, water surface profiles. Froude Number distribution in the whole flow field was obtained. The results showed that flow in the main channel was subcritical flow and flow pattern transformed into supercritical flow gradually while flowing over side weir. The velocity distribution was analyzed according to simulated results. Additionally, discharge formula versus its influence factors were analyzed by regression models with a deviation less than 10%, which met the requirement of flow measurement with discharge up to 40L/s in irrigation districts. Discharge formula that comprises the ratio of the side weir height to the flow depth is simple and easily to be operated, but with lower accuracy. Therefore, it could be chosen when high accuracy is not necessary but within the requirement range. The discharge formula included both Froude number and the ratio of the side weir height to the flow depth is of high accuracy with an average relative error of 1.51%. Taken together, it is concluded that side weir, with simple shape, is very useful device for flow measurement. The results in this study provide references for side weir application in flow measurement, which may stimulate further investigations on new types of side weir with different hydraulic characteristics. Acknowledgment This work was supported by the National Key Research and Development Program of China (2016YFC0400203） and the Special Fund for Agro-scientific Research in the Public Interest of China (201503125). References [ 1 ] Valipour M. Evolution of irrigation-equipped areas as share of cultivated areas. J. Irrig. Drain. Eng. ASCE 2(1)(2013) 1-2. [ 2 ] Valipour M. Increasing irrigation efficiency by management—strategies: cutback and surge irrigation. J. Agricultural and Biological Science. 8(1) (2013) 35-43. [ 3 ] Valipour M. Use of surface water supply index to assessing of water resources management in Colorado and Oregon, US. J. Advances in Agriculture, Sciences and Engineering Research. 3(2) (2013) 631-640. [ 4 ] Valipour M, Montazar A.A. An evolution of SWDC and WinSRFR models to optimize of infiltration parameters in furrow irrigation. J. Sci. Res. 69 (2012) 128-142. [ 5 ] Yannopoulos S I, Lyberatos G, Theodossiou N, etc. Evolution of water lifting devices (pumps) over the 9

centuries worldwide. J. Water. 7 (2015) 5031-5060. [ 6 ] Valipour M. Global experience on irrigation management under different scenarios. J. Water and Land Development. 32(Ⅰ-Ⅲ) (2017) 95-102. [ 7 ] De Marchi G. Essay on the performance of lateral weirs. J .L’Energ Electrica. 11(11) (1934)849. [ 8 ] Q.M. Chen, P.Z. Xie, R.Q. chen, et al. Experiment on hydraulic characteristics of side weir. J. Journal of Fuzhou University. 19(00) (1979) 26-29. [ 9 ] Eminem dew SRamah. Flow over side weir in trapezoidal channels. J. Irrig. Drain. Eng. ASCE 112(2) (1988) 61-64. [ 10 ] Muslu.Y. Numerical analysis for lateral weir flow. J. Irrig. Drain. Eng. ASCE 127(4) (2001) 246-253. [ 11 ] Cosar.A, Agaccioglu.H. Dsicharge coefficient of a triangular side-weir located on a curved channel. J. Irrig. Drain. Eng. ASCE 130(5) (2004) 410-423. [ 12 ] Fiaz Aghayari, Tooraj Honar, Alireza Keshavarzi. A study of spatial variation of discharge coefficient in broad-crested inclined side weirs. J. Irrig. Drain. ASCE 58 (2009) 246-254. [ 13 ] M.Emin Emiroglu, Nihat Kaya, Hayrullah Agaccioglu. Discharge capacity of labyrinth side weir located on a straight channel. J. Irrig. Drain. Eng. ASCE 136(1) (2010) 37-46. [ 14 ] Omer Bihan, M.Emin Emiroglu, Ozgur Kisi. Application of two different neural network techniques to lateral outflow over rectangular side weirs located on a straight channel. J. Advances in engineering software. 41(6) (2010) 831-837. [ 15 ] ME.Emiroglu, H Agaccioglu, N Kaya. Discharging capacity of rectangular side weirs in straight open channels. J. Flow Meas. Instrum. 22(4) (2011) 319-330. [ 16 ] Sara Bagheri, Heidarpour, Manouchehr. Characteristics of flow over rectangular sharp-crested side weirs. J. Irrig. Drain. Eng. ASCE 138(6) (2012) 541-547. [ 17 ] Aydin, M.cihan. CFD simulation of free-surface flow over triangular labyrinth side weir. J. Advances in engineering software, 45(1) (2014) 159-166. [ 18 ] M.Cihan Aydin, M.Emin Emiroglu. Determination of capacity labyrinth side weir by CFD. J. Flow Meas. Instrum. 29 (2013) 1-8. [ 19 ] M.Cihan Aydin, Mualla Ozturk, Ahmet Yucel. Experimental and numerical investigation of self-priming siphon side weir on a straight open channel. J. Flow Meas. Instrum. 45 (2015) 140-150. [ 20 ] Ismail Aydin, A.Burcu Altan-Sakarya, Cigdem Sisman. Discharge formula for rectangular sharp-crested weirs. J. Flow Meas. Instrum. 22(2) (2011) 144-151. [ 21 ] S.Bagheri, A.R.Kabiri-Samani, M.Heidarpour. Discharge coefficient of rectangular sharp-crested side weirs. J. Flow Meas. Instrum. 35 (2014) 109-115. [ 22 ] Novak P, Cabelka J. Models in hydraulic engineering, Pitman, London, UK, 1981. [ 23 ] Henderson F M. Open channel flow. Englewood Cliffs. Prentice-Hall, 1966. [ 24 ] F.J. Wang. Computational Fluid Dynamics Analysis, Tsinghua University Press, Beijing, China, 2004. [ 25 ] C.D. Wang. Water measurement Technique and Measure, Water & Power Press, Beijing, China, 2005. [ 26 ] H.X. Lv, G.X. Pei, L.X. Yang. Hydraulics, China Agriculture Press, Beijing, China, 2002. [ 27 ] Valipour M. Number of Required Observation Data for Rainfall Forecasting According to the Climate Conditions. J. Scientific Research. (74)(2012) 79-86. [ 28 ] Valipour M. Application of new mass transfer formulae for computation of evapotranspiration. J. Appl Water Eng Res. 2(1)(2014) 33-46. [ 29 ] Valipour M, Sefidkouhi MAG, Raeini-Sarjaz M. Selecting the best model to estimate potential evapotranspiration with respect to climate change and magnitudes of extreme events. J. Agri Water Manage. 180(2017) 50-60. [ 30 ] Valipour M. Ability of Box-Jenkins Models to Estimate of Reference Potential Evapotranspiration. J. Agric. Vet. Sci. 1(5)(2012) 1-11. 10

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Highlights 

Experiments and simulations are combined to study hydraulic performances of the trapezoidal side weir.



Velocity distributions are studied in detail.



Discharge coefficient formulas with simple form suitable for different situations are obtained.

11