علیرضا وطن خواه

Allergic rhinitis is an inflammatory disease of the nasal mucosa that can significantly affect the patient's daily life. Therefore, the present study was designed and conducted with the aim of investigating the effect of cellulose powder and Cromolyn sodium in controlling the symptoms of allergic rhinitis and the quality of life of patients, as well as its relationship with CT scan findings.

The present study is a clinical trial that was conducted on patients with allergic rhinitis who were referred to the ENT clinic of Baghiy A. (Aj). The study was conducted as a random and single-phase study in two groups (50 people for each group) using Cromolyn spray with a dose of 3 puffs per day and nasal spray with a dose of 3 puffs per day for 6 weeks in patients. RQLQ quality of life questionnaire, nasal endoscopy score based on Lund criteria, Kennedy score, and visual analog scale (VAS) was completed. Also, in this study, patients with a clinical diagnosis of allergic rhinitis were selected for a CT scan of the Paranasal sinuses without medical treatment. They were referred to the CT scan departments of Baqiyatullah University of Medical Sciences and underwent a Paranasal CT scan and indicators such as polyps, mild mucosal thickening without obstruction, increased bone density of the sinus wall, septal deviation, inferior corneal hypertrophy, and Conca Bellaza were investigated. Then, the findings of the CT scan were reported blindly by only one radiologist. The data collected from both study groups were compared by the respective statistical tests. The significance level for data difference was considered 0.05.

The severity of nasal congestion after 6 weeks of treatment was 2.27 ± 0.97 in the sodium Cromolyn group and 4.61 ± 1.1 in the cellulose powder group. There was a significant difference in the mean severity of nasal congestion after treatment between the two groups. (P=0.03). Statistical analysis showed that the intensity of sneezing and also the intensity of runny noses in both groups improved significantly after the completion of the treatment. (P=0.00). The mean RQLQ score after treatment was 22.525 ± 5.71 in the sodium Cromolyn group and 25.85 ± 2.91 in the cellulose powder group. There was no significant difference between the two groups in the average RQLQ score after treatment. (P=0.073). In this study, the relationship between CT scan findings in both groups of patients before and after the use of both drug categories was investigated. In this study, both groups of patients underwent CT scans before starting the treatment, and the most common findings in both groups in the CT scan were polyps, mild mucosal thickening without obstruction, increased bone density of the sinus wall, and septal deviation. hypertrophy of the inferior cornea and Conca Blesa, also according to the obtained results, no statistically significant difference was found between the findings of the CT scan in both groups (P-value<0.05).

Based on the results of this study, it can be concluded that nasal decongestant can be used as an effective drug without complications in the treatment of allergic rhinitis patients due to the improvement of symptoms and quality of life. But in terms of effectiveness, it is not more effective than Cromolyn. On the other hand, there is no correlation between CT scan findings among patients with allergic rhinitis, and it can be said that the use of radiology and especially CT scans is not recommended for allergic rhinitis.

The increase of flow velocity and Reynolds number in coarse porous media and the subsequent violation of Darcy's law, force to analyze the flow based on nonlinear relations of hydraulic slope and flow velocity. So, it is necessary to study nonlinear relationships more accurately. The purpose of this study was to investigate the performance of fractional-order model and the effect of conformable derivatives on improving the relationship between flow velocity and hydraulic gradient. Therefore, by determining the acceptable range for the fractional-order model, a nonlinear model based on conformable derivatives of the Izbash equation for the fully developed turbulent flow was presented and solved analytically and the parameters of the proposed model were determined using laboratory data analysis. The optimal values of the model parameters including coefficient a and the order of fractional derivative α, which can be varied in the range of (0-2), were calculated for each laboratory data set. The results were compared with the experimental data and the analytical solution of Izbash equation and a good agreement was found to the non-Darcian flow laboratory data. Moreover, using dimensional analysis method, Reynolds number was introduced as an effective factor on α coefficient and a suitable relationship was observed between the order of fractional derivative α and Reynolds number indicating the hydraulic concept of fractional-order model. According to the present study, the fractional order α is not only a fitting coefficient, but it represents a physical concept.

The book "Jame chr(chr('39')39chr('39'))al-Asrar va manba ‘al-anvar " is the most important mystical book of Seyyed Haidar Amoli, a Shiite mystic and commentator of the eighth century AH. In this book, Seyyed Haidar applies and proves the most fundamental subject of Islamic mysticism, which is "monotheism and monotheistic" based on the original Shiite sources, that is revelation, narration and reason and  Ibn Arabichr(chr('39')39chr('39'))s discovery  on the issue of "guardianship" Considers it incomplete and the result of religious prejudice and by believing in the three levels of religion, he considers "canon (religious law), religious path, and Truth" as the only hierarchical truth  and he believes they are a single truth and are not separate and ultimately limit original mysticism to the right religion of Shiism. Therefore, one of the most important motives for writing this book was to explain the "truth of Shiism" and to defend the legitimacy of Shiite beliefs. In designing all mystical issues, he uses revelation and reason and discovery based on the original Shiite thought with the focus on the prophetic and Alavi " guardianship ", so it can be said that the ruling spirit of this book is the principles of Shiite ijtihad.The forthcoming research, in addition to the most important characteristics and principles of Shiite mysticism, emphasizes this valuable book such as "Belief in Existential Monotheism, Belief in the Equality and Objectivity of Twelver Shiites with True Sufism, Reliance of Shiite Mysticism on the Source of Revelation and Narration, Belief in rationality of Mysticism Shiism and the adaptation of taste to reason and…” In area, the principles of mystical epistemology have been extracted, analyzed and explained.

Accurate water measurement is one of the key factors for reduction of agricultural water consumption, distribution integrity and delivery management in irrigation networks. In recent years, there has been a significant advance in flow measurement devices, but the usage of these devices is limited due to the high cost, special maintenance conditions and the need for skill expertise. Water structure used in this study is a new form of flow measurement flume that installed along the channel and has cylindrical and conical shape walls. The crest matches the channel's floor thus in this measuring structure, the control section happens only by transversal constriction. The new flumes are simple in shape and easily applicable in irrigation networks and they have not sedimentation problem. The amount of energy loss and consequently the upstream backwater in this structure is low. This structure controls the flow by creating critical flow in constriction section and will be able to measure flow discharge. In this study, the flow characteristics through the cylindrical and conical flumes have been studied theoretically and experimentally, and several equations have been developed for flow discharge estimation in rectangular open channels.

In this study, the fractional-order differential equations in range of (0,1) were used to model the water surface profile under Darcy's law condition in porous medium for a fully developed turbulent flow. The developed equation is solved analytically. The laboratory model used in this study consists of a coarse-grained porous medium with 6.4 m length, 0.8 m width and 1 m height, including rounded corner materials, which are tested for different flow rates and three longitudinal slopes of 0, 4, 20.3%. Then, parameters of model and porous media were calibrated based on laboratory data. In order to evaluate the proposed analytical solution, the obtained results from fractional-order differential model were compared with the laboratory data. The results showed a satisfactory agreement with experimental data of water surface profile (seepage line) in all three slopes. The maximum error of the proposed model is 3.5% compared to the experimental data. It can be concluded that the proposed method can provide better description of water surface profile analysis under non-Darcy flow conditions as compared to Darcy model in porous media.

In practical applications, for instance, at the downstream of hydraulic structures, in some cases the width of the basin may be larger than the upstream supercritical flow (sudden expansion in flow section). In such cases, an expanding hydraulic jump with symmetrical or asymmetrical shape will be developed at the downstream. Under the design of three parallel gates, the operation of the side or middle gate can be lead to the asymmetrical or symmetrical hydraulic jump, respectively. According to the position of jump toe, expanding hydraulic jump can be classified into four types. The present study focuses on a T-shaped hydraulic jump which the toe is established at the beginning of the divergence section.Most of the previous studies are related to the symmetrical expanding hydraulic jump. In this case, the downstream diverging channel is symmetric on the central axis of the channel. However, a systematic study investigating the effect of symmetry and asymmetry on the expanding hydraulic jump was not found in the literature. In this study, using the momentum principle, some theoretical equations were derived to determine the sequent depths ratio of symmetrical and asymmetrical expanding hydraulic jump. Also, some regression relations were proposed to estimate the length of expanding hydraulic jump. The new proposed equations were also extended for the presence of a sill. The equations were calibrated using available experimental data from this study and the literature. This research also considered the characteristics of expanding hydraulic jump under the symmetrical and asymmetrical operation of parallel gates.

To calibrate the new proposed relations and investigate the effects of different parameters on the expanding hydraulic jump characteristics, two experimental data sets were used. In addition to the data set from Bremen (1990), the experimental data from the present study were used. The data were collected from a hydraulic model of three parallel radial gates for operating the side or middle gate which corresponds with the asymmetrical or symmetrical expanding hydraulic jump, respectively. The experiments provided a wide range of different parameters as the approaching Froude number, hydraulic jump length, sequent depths ratio, divergence ratio, sill height and relative length of gate separator wall.

Equation (4) was developed to determine the ratio of the sequent depths of expanding hydraulic jump based on the Momentum equation. For the presence of a sill, a combination of Equations (4), (7) and (8) can be used to calculate the ratio of sequent depths under the asymmetric and symmetric developments, respectively.Determining the ratio of the sequent depths requires the calculation of the adjacent water depths of the closed gates. For this purpose, in addition to developing the regression equation (Equation 13), Equation (12) was proposed which based on the calculation of the hydraulic jump profile. It was observed that under the calibration range, the regression equation is more accurate. However, Equation (12) is recommended for the range outside of the experimental observations. The results showed that:As the divergence ratio increases, the ratio of sequent depths approaches to the classic hydraulic jump.By decreasing the relative length of the gate separator wall and decreasing the width of the gate on the downstream channel width, the relative depth at the side gate and consequently the ratio of the sequent depths will decrease.For the lower length of separator wall and under operation of the middle gate, more lengths are needed to develop the jump than the side gate. However, as the length of the separator wall increases, the length and sequent depth of hydraulic jump due to the side gate increases on the middle gate.In the presence of a sill, the relative length of hydraulic jump decreases and the ratio of secondary depths increases.It was observed that the hydraulic jump due to the operation of the middle gate leans toward the left or right side of the channel due to oscillatory behavior.Under operating the middle gate and in the absence of a sill, an asymmetric hydraulic jump is formed in the channel face when the length of the separator wall is less than 38% of the classical hydraulic jump length. For the presence of a sill, the minimum length of the separator wall decreases to about 26%.By decreasing the initial depth of the hydraulic jump on the width of the gate and converting the output jet into a linear jet, the relative development length will increase.
As the sill height increases, the difference in the depths attached to the side gates will decrease and the hydraulic jump will develop more symmetrically.As the relative height of the sill decreases, the minimum length of the separator wall to form a symmetrical hydraulic jump in the flanks, increases.

This research developed a set of theoretical and regression relationships for estimating the length and sequent depth ratio of expanding hydraulic jump. Moreover, the effects of sill height, divergence ratio and the length of the gate separator wall, were investigated. This study compares the effects of side and middle gate operations based on the variation of jump length and sequent depth ratio. The results can be used as a guide for the hydraulic structures operators to reduce the asymmetric severity of the expanding hydraulic jump and achieve the complete development under the minimum length.

One of the most commonly used devices for flow measurements in open channels is the flume, in which the flow velocity increases due to the lateral contraction, raising the bottom of the channel, or a combination of both them. SMBF is a flume with the above mentioned properties, having two semi-cylinders on the side walls of the channel that contract the cross-sectional area of the flow. In this study, the SMBF flume has been studied for measuring the flow in free and submerged flow conditions. Using the experimental data (575 runs) of two rectangular channels, and using eight SMBF flumes, the proposed discharge equations were examined for the wide ranges of flow discharge, upstream depth, and contraction ratio. In the present study, based on the numerical and experimental analysis, and by measuring the velocity distribution at the throat section, non-uniformity of velocity distribution and depth in the contracted section, as well as the two-dimensional nature of flow were studied. Then, by considering the flow correction coefficients in the throat section and applying them into the energy equation, an equation was developed for estimating the flow discharge‎ under free flow conditions. Also, two equations were developed to determine the submergence threshold (as a function of upstream depth and throat width) and for the discharge estimation under submerged conditions. The mean absolute relative error of the estimated flow discharge of the SMBF flumes in free flow conditions and based on three experimental data series (channel 1, channel 2, and other researcher’s data) were respectively estimated to be 2.82, 3.19 and 1.52%. Additionally, the mean absolute relative error of the estimating flow discharge in the submerged conditions was 5.51%. The results showed a feasible application of SMBF structure, as a portable measuring instrument under free and submerged conditions.

The existing Muskingum models vary only in the form of the storage equation. So far, for accounting the nonlinearity characteristic of flood wave, the form of the storage equation has been modified based on the experience and in a trial and error manner in order to capture the overall flood propagating characteristics more accurately. One of the theoretical based method for considering the nonlinear characteristics in Muskingum model is to use the fractional derivative in the continuity differential equation. This study presents a new Muskingum model in which the linear storage equation and the continuity equation with fractional derivative are used. As shown in this study, the new model can simulate flood waves with both linear and nonlinear behaviors. The proposed Muskingum model with fractional derivative order was implemented and tested on three different sets of flood data. The results of this study indicate that the proposed Muskingum model improves the results and estimates the flood wave characteristics more accurately than the traditional linear Muskingum models.

The Present study introduces the slit and solid semicircular flap plates for flow measurement in horizontal open circular canals under free flow conditions. This structure consists of a semicircular plate which is installed and hinged from its diameter along a circular canal. The deviation generated by the water flow on the plate is a function of hydraulic characteristics of flow, the geometry of the structure and flow discharge. This simple measuring structure is portable and can easily be installed in circular canals and be used with acceptable precision. In this study, based on the theoretical and experimental studies of the passing flow through the semicircular flap plate, some equations were developed for estimating the flow in circular canals via the dimensionless discharge-critical depth relation. In order to calibrate the proposed equations, the laboratory data were collected and used. In addition, to estimate the passing flow through the flap plate, an explicit relationship was developed to compute the dimensionless critical depth and discharge. The dimensionless critical depth-discharge method used in this study is able to estimate the flow discharge through the semicircular plates with an average error of 3%. Due to the low average errors of the proposed discharge equations for the semicircular flap plate (an average error of 3.6% without considering the Reynolds number and an average error of 3% by considering the Reynolds number), this structure is suggested as a discharge measuring structure in circular open canals.

Sluice gates are designed and used in Ogee spillways with high height (regulator dams) or low height (as sill) for better controlling the flow. In latter case, according to different combinations of weir geometry, gate opening, upstream and downstream flow depths, four different flow conditions are recognizable: (a) free uncontrolled flow, (b) submerged uncontrolled flow, (c) free controlled flow, and (d) submerged controlled flow. Determination of change threshold of these flow condition is useful for choosing the proposed discharge equations in any situation. In current research, using the experimental data gathered from two Ogee spillways with different height in this program and using the data gathered from typical spillway structures in central and southern Florida water-control project, different equations for determining the change threshold and flow discharge in four different flow conditions are developed. In free uncontrolled flow condition, the proposed discharge equation has an average relative error of 1.95% while in free and submerged controlled flow condition, the proposed discharge equations have the average relative errors of 2% and 5% respectively. Results showed that the change threshold of uncontrolled flow into controlled flow occurs when upstream flow depth increases about 1.46 times the gate opening. Furthermore, the relative submergence threshold and flow discharge increase by increasing the downstream flow depth and decreasing the upstream flow depth.

Side weir is one of the diversion structures, which widely used in irrigation and drainage networks, flood protection, urban sewage systems and water level control. The flow over the side weirs is a typical case of the spatially varied flow with decreasing flow discharge. In this study, the flow characteristics over the circular-crested trapezoidal side weir located in rectangular channels is experimentally investigated under subcritical flow conditions. In this research, the conventional weir theory with three different reference depths (y1, yavg and ycenter) for computing the weir head was used to evaluate the proposed discharge coefficient and discharge equations. Based on the experimental results, the discharge coefficient is a function of upstream Froude number, the ratio of upstream flow depth to the crest diameter, and side slope of the weir. The comparison between the experimental data and computed results indicated that the conventional weir theory with the average flow depth as the reference depth with an average error of 3.6% is the best relationship for assessing the discharge coefficient. Thus, this method is suggested for practical purposes.

Flow over side weirs has been the subject of many studies. Most of these studies related to sharp crested side weirs with rectangular cross section and less attention has been given to the discharge coefficient over the broad-crested side weirs with trapezoidal cross section. In this research a comprehensive laboratory study including 187 tests has been conducted to investigate the discharge coefficient over the broad-crested trapezoidal side weir under subcritical flow regime. Since a complete analytical solution of the governing equation for a side weir is not possible due to nonlinearity and the many variables involved, in this research water surface profile along the side weir is computed by using the fourth order Runge–Kutta method. By analyzing experimental data and using dimensional analysis as well as statistical analysis, some relationships in order to estimate the discharge coefficient were proposed. It was founded that the discharge coefficient of flow depends on the Froude number, the ratio of initial depth to crest width and the side slope of the weir. The mean absolute percentage error of proposed relationship is about 4% and indicates that the numerical method is very accurate.

Most of the previous studies related to radial gates are focused on the estimation of discharge from the gates as a flow measurement structure. However, determination of the gate opening for passing a certain value of the discharge is rarely considered in previous studies as a regulator structure. The present work presents some theoretical equations for explicit estimation of the outflow from the gate (first problem), and gate opening (second problem) for free and submerged flow conditions by combination of Energy and Momentum principles. For any problems, it was developed some criteria to identify flow conditions These equations were calibrated and validated by means of 2657 experimental records retrieved from research conducted on three types of radial gates. The paper would present an analytical approach to illustrate the reliability of proposed equations for estimation of discharge and the opening of the gate by taking benefits from the mean absolute relative errors which observed to be 1.94% and 2.67, respectively. It was noted that the used criteria conform with 99.6% and 98.8% of all observations at first and second problems, respectively. The results show that the tailwater depth under distinguishing limiting decreases by increasing in the gate lip angle and the ratio of turnnion pin height to the gate arm radius. Also, the hard rubber bar gate tends to operate under free flow condition in a wider range in comparison with two other gates.

Discharge measurement by sluice gates is one of the classical issues in hydraulic engineering. Based on the energy conservation relation, this study presents a novel method for estimating the discharge coefficient of sluice gates under free and submerged flow conditions. This method gives the discharge coefficient of sluice gates only as a function of upstream depth and bottom pressure measured by manometers located under the gate lip and is independent of flow conditions (free and submerged), gate opening and tailwater depth. For evaluating the applicability of the proposed equation in this research for estimating the flow discharge, the experimental results (418 runs) of two sluice gates with 25 and 40 cm widths are used in the conditions of presence and absence of end baffle blocks for both free and submerged flows. Independency of discharge coefficient from the tailwater depth has important advantages such as: continuous estimation of discharge coefficient under free and submerged flow conditions using a unified equation and higher accuracy at the lower submergence. Also being independent of tailwater depth makes easy flow estimation even at the presence of baffle blocks on the stilling basins. The results show that, applying the energy loss coefficient in the proposed equation decreases the mean absolute relative errors to 0.4% and 2.6% for free and submerged flow conditions respectively. Also the proposed equation has a relative error less than 5% under submerged flow conditions. The proposed method is very sensitive to bottom pressure head especially under higher submergence levels.

Weir is one of the most applicable instruments for flow control and measurement in open channels. Accurate measurement of discharge in irrigation channels is vital for irrigation management. Weirs are designed as control sections for providing a unique relationship between the discharge and water head. In current study, theoretical and experimental characteristics of flow through a weir located in a horizontal circular channel were investigated. Choosing of this structure is due to lack of adequate studies on governing hydraulic equations of this kind of channels and its practical characteristics. In this research, discharge through the weir located at the end of a horizontal circular channel was developed from a theoretical viewpoint, and then calibration of this theoretical discharge equation was done via the discharge coefficient. The experimental data obtained in the study were also used to develop an empirical discharge coefficient relationship.
Theoretical discharge equation:The discharge equation of the circular weir ends up incomplete elliptic integrals of the first and second kinds, which are not very suitable for practical purposes due to their complexity. The theoretical discharge over the weir, Qt, can be expressed as:in which F(a,b) is approximated using the method of undetermined coefficients as:where g is the gravitational acceleration, h is the flow depth above the weir crest, D is the channel diameter, , , , and P is the weir height.
Introducing the discharge coefficient, Cd, yields the following equation for actual discharge, Q, of the weir.
Experimental setup and discharge coefficient equation: Determination of discharge coefficient, Cd, needs measuring the actual discharge (experimental or field data). The experiments were performed at the hydraulic laboratory of the Irrigation and Reclamation Engineering Department, University of Tehran. In order to collect experimental data, the weir was installed at the end of two horizontal circular channels with nominal diameters of 200 mm and 300 mm, and numerous measurements of different parameters that may have effect on discharge coefficient were carried out. An opening was provided on top of the pipes for flow head measurements by the point gauge. Water head over the weir crest was measured at a distance of 0.45 m upstream of the weir section. The weir plate was made of 10-mm-thick PVC sheet with a crest thickness of about 1 mm, and the downstream edge bevelled to a 45° angle (sharp-crested weir). For water heads over the weir crest smaller than 1.5 cm, in some cases clinging flow did occur and thus there was no atmospheric pressure under the lower nappe. Though, for heads greater than 1.5 cm a clear lower nappe profile with atmospheric pressure underneath was formed. Effects of surface tension and viscosity forces on the discharge coefficient, Cd, became pronounced at low water heads. Viscous and surface tension effects on discharge coefficient are neglected in this research. This is owing to operating range of the weir (minimum water head of 2 cm), which forbids surface tension effects and eliminates viscous effects. The experimental coefficient of discharge is computed for each data set collected in this study for known values of D, h, P and Q. A total of 350 tests were conducted to collect the data in the discharge ranges of 0.5 and 45 l/s. Suitable empirical equations for discharge coefficient were proposed using the 70% of the experimental data, and remaining data (30%) were used for validation procedure.
Proposed empirical equation for discharge coefficient: Using the curve-fitting technique, the following equation is obtained for CdThis empirical equation is valid for 0.095≤h/P≤1.8, 0.27≤P/D≤0.73 and 0.05≤h/D≤0.56. The assumptions made in deriving the above empirical equation of discharge coefficient are that the channel slope is horizontal, the flow is free and surface and viscous tension effects on Cd are negligible. A comparison of the experimental discharge coefficient with computed ones using the proposed empirical equation for all of the experimental data, the calibration data set and the validation data set showed that the computed discharge coefficient values are well within ±5% of the observed data for all three data sets. The average relative error of computed discharge coefficient using the proposed empirical equation for discharge coefficient Cd compared with the observed values is less than 5% for 95% of all experimental data. The results of this study reveals that a weir with low flow height is more sensitive to water flow depth, and weirs with more height are less sensitive to upstream flow head variation and thus are more reliable for flow measurement.

Side or lateral weir is a flow measurement structure that is extensively used in irrigation and drainage networks and sewer systems. The main channel cross-section and side weir shape completely modify the flow conditions. Up to now, many studies have been conducted on side weirs. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs. This study focuses on a circular sharp-crested side weir located in a rectangular main channel in subcritical flow regime. This kind of side weir has some advantages, in comparison to other general weir types. Since the height of this side weir varies along its length, it can control flood better than other side weirs in flood conditions. In addition, because of its circular shape, it has a greater discharge coefficient.
The governing equation of the circular sharp-crested side weir has no analytical solution and thus should be solved by numerical methods. In order to simplify the solution, the equation of inline circular weir with discharge coefficient as a calibration parameter is used. The reference flow depth which should be used in this equation is an important point. In this study, three reference depths were considered (average depth 0.5(y1), center depth and initial depth y1).
In this research, the equation of conventional circular weir presented by Vatankhah (2010) is used for circular sharp-crested side weir:where Qa=actual discharge; Cd = discharge coefficient; g = gravitational acceleration; and η=H/D, with H being flow depth above the circular sharp-crested weir of diameter D.
For circular sharp-crested side weir, effective non-dimensional parameters were determined using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient:where Fr= Froude number and B= main channel width.
The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height which was installed on a frame. The lateral channel has a length of 6 m, width of 0.25 m, and height of 1 m that was set up parallel to the main channel; the walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 123 experiments on circular sharp-crested side weirs were carried out.
Different depths were considered as the reference depth. According to the experimental analysis, the discharge coefficient is a function of the upstream Froude number and the dimensionless ratio of its diameter to the main channel width.
The proposed empirical equations for discharge are as: (Average depth 0.5(y1) as the reference depth)
(Center depth as the reference depth)
(Initial depth y1 as the reference depth)
The average errors of the proposed equations are less than 2.4%, and only 5.5% of the experimental data have error more than 5% if the averaged and center depths are considered as the reference depth. However, 8.1% of the experimental data have error more than 5% if the initial depth is used as the reference depth.
In this research, the characteristics of the circular sharp-crested side weir overflows in subcritical flow regime are discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and carefully analyzed to develop accurate and simple discharge equation. The results showed that the most efficient section for measuring the water surface profile is located on the center line of the approaching channel. It was also found that for the circular sharp-crested side weir, the discharge coefficient depends on the Froude number and the ratio of weir diameter to the main channel width. In this study, the conventional circular sharp-crested weir theory has been used in order to evaluate the discharge coefficient and provide a side weir discharge equation. For this purpose, three reference flow depths were considered for conventional weir (average depth 0.5(y1), center depth and initial depth y1), and for each flow depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that the average and center flow depths result in accurate outcomes for estimating the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equations is less than 2.4%. Thus, these equations are proposed for practical use.

Side weir is a flow control structure that used extensively in irrigation and drainage networks and sewer networks. In this research, a study with 162 experiments has been done on sharp-crested circular side weir. Since the height of this side weir varies along its length, this feature enables it to control flood better than rectangular side weir in different flood conditions. The governing differential equation of circular side weir has no analytical solution, and thus it is necessary to use numerical methods to solve it. Since numerical methods have computation cost, normal weir equation and linear assumption of water surface profile are used to solve the problem. Lastly, by doing three other experiments under completely different conditions, it was found that the method of considering linear water surface profile has less error in comparison with other methods used in this research.

A free overfall offers a simple device for flow discharge measuring by a single measurement of depth at the end of the channel yb which is known as the end depth or brink depth. When the bottom of a channel drops suddenly, the flow separates from sharp edge of the brink and the pressure distribution is not hydrostatic because of the curvature of the flow. In channels with subcritical flow regime, control section occurs at the upstream with a critical depth (yc). Although pressure distribution at the critical depth is hydrostatic, the location of the critical depth can vary with respect to the discharge value. So, the end depth at brink is offered to estimate the discharge. A unique relationship between the brink depth (yb) and critical depth (yc), known as end-depth ratio (EDR = yb/yc), exist. Since a relationship between the discharge and critical depth exists, the discharge can ultimately be related to yb. However, when the approaching flow is supercritical, critical section does not exist. Therefore, the discharge will be a function of end depth and channel longitudinal slope.
In current study, an analytical model is presented for a circular free overfall with different flat base height in subcritical and supercritical flow regimes. The flow over a drop in a free overfall is simulated by applying the energy to calculate the EDR and end depth-discharge (EDD) relationship.
End-depth-discharge relationship: The flow of a free overfall in a channel can be assumed that is similar to the flow over a sharp-crested weir by taking weir height equal to zero. It is assumed that pressure at the end section is atmospheric, and also streamlines at the end section are parallel. To account for the curvature of streamlines, the deflection of jet due to gravity, the coefficient of contraction, Cc, is considered. At a short distance upstream the end section, the pressure is hydrostatic. By applying the energy equation between end section and control section which is at upstream the end section, the flow depth at the end of the channel yb in terms of depth at the control section can be determined.
Subcritical flow regime: In this case, the approach flow to the brink is subcritical for negative, zero and mild bed slopes with critical depth at the control section. Using the definition of the Froude number at critical depth, the discharge can be determined. As the explicit relationship between discharge and depth at the brink don’t exist, a relationship should be presented through regression analysis between discharge and yb using the different values of yc over the practical range of 0.01 to 0.84. In this study, below explicit equation is presented for computing Q*(dimensionless discharge) in terms of ( ): Where d is channel diameter, is the ratio of bottom elevation to the channel diameter and . This equation can be used for different values of over the practical range of 0.06–0.6.
Supercritical flow regime: A critical flow occurs upstream of the free overfall under the subcritical approach flow. However, no such critical flow occurs in the vicinity of the overfall under supercritical flow regime. Therefore, the Manning equation for known value of channel bed slope and Manning’s coefficient is exercised to derive the discharge relationship under the supercritical flow regime. Since an explicit equation for discharge in term of yb is impossible, a direct graphical solution for discharge for known end depth, channel bed slope, and ratio of bottom elevation has been provided for supercritical flow regime.
The free overfall in a circular channel with flat base has been simulated by the flow over a sharp-crested weir to calculate the end-depth ratio. This method also eliminates the need of an empirical pressure coefficient. The method estimates the discharge from the known end-depth. In subcritical flows, the EDR has been related to the critical-depth. On the other hand, in supercritical flows, the end-depth has been expressed as a function of the longitudinal slope of the channel using the Manning equation. The mathematical solutions allow estimation of discharge from the known end-depth in subcritical and supercritical flows. The comparisons of the experimental data with this model have been satisfactory for subcritical flows and acceptable for supercritical flows.

In this study, an explicit equation is presented for estimating the height of the end sill in the trapezoidal stilling basin based on the energy equation. In addition to the experimental results were compared with energy and momentum methods which have been solved by numerical methods. Evaluation results indicate proper coordination between experimental and computational data and confirmed that the presented explicit equation can compute end sill height with suitable accuracy. In recent decades, several studies aimed at understanding the function of hydraulic jumps in trapezoidal sections have been made Forrester and Skrinde (1950) to find an analytical equation based on the Froude number, initial depth, sequent depth and sill height for controlling jump in rectangular sections which used rectangular broad-crested weir equation for determining discharge which was created by Barker and Doeringsfeld (1941). Achour and Debabeche 2003) investigated the effects of broad-crested end sill on the U-shaped sections as well as the effect of the sharp-crested end sill on the triangular sections with the apex angle of 90°, by comparing the theoretical and experimental equations in U-shaped sections. They also found that the required sharp-crested end sill for controlling the hydraulic jump with the same conditions should be slightly taller than broad-crested end sill in U-shaped cross sections. Achour and Debabeche (2003) presented an explicit relationship in rectangular sections to find the minimum broad-crested end sill height necessary to control the hydraulic jump which indicated good agreement with the results of Forrester and Skrinde (1950). If a broad-crested end sill placed on the supercritical flow path in the stilling basin, hydraulic jump is formed. The minimum height necessary for the sill according to the specific energy concept can be calculated. In this case, due to the existence of critical depth on the sill, this section will act as a control section. To evaluate the results of the proposed explicit equation to determine the end sill height, a number of tests were carried out. Experiments were done in a horizontal channel with symmetrical trapezoidal cross-section, and with side slopes z=0. 5, 1, 1. 5, Length of 3 m and a width of 5. 0 meters to measure the characteristics of flow jumps in the discharges range of 19. 3 «To slow down and measure the input flow in laboratory model, upstream primary reservoir, with dimensions of 1. 25 m wide, 1 m long and 1 m high were designed and built. Inlet water flow to model supply through the circulated flow system with the closed circuit pipes in the laboratory, and through the branch of pipe near the model was connected to the first tank. To calm the approaching flow to the weir, a mesh with 1. 25 m width and 1 meter height was used. Discharges measured with a calibrated weir in upstream tank. With the crossing of water over the weir, the flow was entered to supply-height reservoir. The purpose of constructing this reservoir was providing the required energy for the formation of the hydraulic jump with desired Froude number. Initial and sequent depth was measured with an accuracy of 1. 0 mm by a point gage. In order to create jump without the end sills, flow was controlled by a terminal movable valve as a tailgate. For each of the experimental data obtained from the Fr1, in the range of 3Given that the critical depth was created on the broad-creased sill, by writing momentum equation at the section of the sequent depth and sections with critical depth on the sill, the sill height can be calculated. As well as the sill height can be calculated by Bernoulli equation without taking into account the energy loss. Using any of these two methods is needed to solve nonlinear equations implicitly. With the proposed explicit equation, estimation of height end sills is provided easily in terms of the flow characteristics and canal cross sections with high accuracy. The values obtained from the proposed explicit equation for the height of broad-creased end sills with predicted values of energy and momentum equations are approximately the same, and all three methods have little difference with the experimental results. Also, it can be said that this equation can be predicted experimental data with high accuracy and indicates good performance as terms of practicality. In this study, the control of hydraulic jump with broad-creased end sills in trapezoidal sections with three side slope of 1:0. 5, 1:1 and 1:1. 5 was investigated. Flow analysis over the broad-creased sill allowed that the minimum sill height necessary for controlling the hydraulic jumps to be estimated. The results of the comparison of the proposed equation with momentum and energy equations and experimental results showed good accuracy in estimating the required broad-creased sill height to control the jumps in trapezoidal sections. Because there are no more experimental results, presented equation can be used as a guide in designing of energy dissipators to determine the broad-creased sill in trapezoidal sections with the explicit equation. It is noteworthy that the broad-crested sill is superior in comparison with other dissipators hydraulic jump structures, due to its structural stability and lower costs.»

In the present study، hydraulic properties of low pressure drip irrigation systems in lateral pipes were evaluated by mathematical model with the aid of experimental data resulting from testing of tubes available in Iran. In this regard، emitters discharge were measured in different initial heads from 0. 45 to 1. 8 m for laterals with outside diameter of 32 mm with different lengths of 89، 60، 30، and 16 meters and also for laterals with the length of 16 meters and external diameters of 32، 25، 20، and 16 mm. the obtained discharge-head relation was q=1. 955h0. 8421 with R2 of 0. 93. On the basis of the ratio of lateral diameter to its length، two relations were proposed for estimating local loss as a function of Reynolds number with R2 of 0. 95 and 0. 75. Furthermore، experimental results showed that Colebrook-White relation could be used as a good estimation for friction losses. The model was calibrated and evaluated using experimental data and relations which were obtained from experimental results. The model was used for evaluating the effect of different heads، lateral diameters، and length on emitter discharges، which was not possible to evaluate experimentally. The results revealed that the proper length interval in which the uniformity is more than 80% was 40 to 75 meters for laterals with the external diameter of 16 mm under different heads (from 0. 45 to 1. 8 meters). This length interval for laterals with external diameters of 20، 25، and 32 mm was 50 to 100 m، 70 to 150 m، and 80 to 180 m، respectively. Finally، a relation was developed for designing low pressure drip irrigation system.

Side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. Side weirs are also used as an emergency structure. This structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. Lateral outflow takes place when the water surface in the main channel rises above the weir sill. Flow over a side weir is a typical case of spatially varied flow with decreasing discharge. There have been extensive studies on side weir overflows. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. In the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. It was set up parallel to the main channel; walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 121 experiments on trapezoidal side weirs were carried out. For trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow.in which Fr1= upstream Froude number, P= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and T=top flow width of the trapezoidal side weir. Water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. Different elevations in water surface profile depend on the upstream Froude number in the main channel; depth differences in low Froude numbers are at minimum values, and in high Froude numbers are at maximum amounts. The water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. Afterwards, the water level rises towards the downstream of the weir. According to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. According to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. Finally, the general equation was proposed. The general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. The mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5%, respectively. In this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. The results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. It was found that for trapezoidal side weir, the discharge coefficient depends on the Froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. In this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. For this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equation is 2.6%. Thus this equation is proposed for use in practice by water engineers.

Proportional weirs in which the discharge is linearly related to the head are known as linear proportional weirs. Because of unit power of their head, linear proportional weirs are more preferable than other traditional weirs in some situations. In this research, based on theoretical concepts different linear proportional weirs having inverted triangular, chimney and two inverted triangular sections were designed. Then, the weirs were constructed and their linear relationship was examined experimentally. 180 runs were conducted to compile the data in the discharge range between 1 and 8 l/s. The data proved the presence of linear relationships for all the examined weirs. The results are shown that relative error of 50%, 66% and 73% of experimental data for inverted triangular weir, chimney weir and two inverted triangle weir are between 1%±. Also, it is observed that the two inverted triangular weir performed better than that of other two weirs, that is, the two inverted triangular weir data had the minimum deviation from its proposed relationship.

In this study, Hydraulic properties of low pressure drip irrigation systems were studied under laboratory conditions and using of the pipes that exist in Iran. Therefore, effect of various heads from 0.45 to 1.8m was evaluated for lateral pipe with outside diameter 32mm and length of 16, 30, 60 and also the lateral pipe with length 16 and outside diameter of 16, 20, 25 and 32mm, on hydraulic characteristics consist of average emitter discharge, variation coefficient, uniformity and loss. Emitters used in this study were micro-tube with length of 0.7m and outside diameter of 3mm that inserted to the lateral at 1m intervals. Results showed low pressure trickle irrigation system supplied necessary discharge in all of the lateral length and diameters to the end of it. Moreover, examine effect of lateral length and diameter on emitter coefficient uniformity indicated that desirable uniformity obtain in the lateral with length of 89m and outside diameter of 16mm and also the least head.

Accurate measurement of flow in open channels، water transmission and sewage networks is accounted as an important issue in operational management of hydraulic structures. So far، various types of structures such as weirs، orifices، flumes and slide gates have been used to measure the discharge in conveyance structures. Meanwhile، proportional weirs، a type of sharp-crested weirs، have high accuracy، because of their low sensitivity to upstream depth. In the linear type of proportional weirs، the relationship between discharge and head is linear، while in quadratic and logarithmic types، linear relationships are established between discharge and square head، and between discharge and logarithm of head، respectively. In this research، based on theoretical criteria for proportional weirs and also dimensionless design method، three types of linear proportional weir; i. e. chimney cross section، inverted triangle، and inverted two triangles، and two types of quadratic proportional weir; i. e. one-piece and two pieces linear edge، were designed، constructed and installed at the end of a rectangular channel. In this research، about 600 experiments were carried out with discharge range of 2 to 10 l/s to find experimentally the relationships between head and discharge in the above mentioned proportional weirs. Results of experiments showed that discharge coefficient is a function of dimensionless ratio of the head to the weir height، and the dimensionless ratio of the weir crest length to the weir height. Using some of the experimental results، a relation between discharge and flow coefficient obtained for each weir. Comparison of the results obtained from the relationships with the rest of the results from experiments، showed that the average error of the proposed equation is equal to 1. 5 percent، indicating high accuracy of the proposed equations.

Accurate estimation of mean velocity and discharge of open channels is one of important goals in hydraulic knowledge. Application of Manning equation is one of the methods with abundant use for mean velocity calculation. Application of this equation in several cross sections such as circular section is associated with error. In this study, effective hydraulic radius is defined based on cross section shape in Cartesian coordinates. In this definition, the effect of water surface roughness is applied in calculations with respect to a weight factor greater than one. By application of effective hydraulic radius in Manning equation for circular cross section a good accordance was observed between calculated and existed experimental results. Root square means error of relative computational velocity and discharge from the conventional and effective hydraulic radius toward experimental data are 0.14904, 0.08125 and 0.01113, 0.00042, respectively. Results showed that application of effective hydraulic radius has a significant effect on increasing the accuracy of Manning equation compared with conventional hydraulic radius.