Short CommunicationAnalysis of flow through lateral rectangular orifices in open channels
Graphical abstract
Introduction
Side orifices are used to divert flow from main channel to secondary channels and widely used in hydraulic, environmental and irrigation engineering. The flow is diverted from a channel to different fields through prescribed side orifices for the irrigation purpose. In water and wastewater treatment plants, side orifices are often used to distribute incoming flow to parallel process units such as flocculation basins, sedimentation tanks, and aeration basins [14]. The mechanics of flow through a single orifice located in the side of open channels have been studied by many researchers. Detailed study on side rectangular orifice or slot has been carried out by Gill [4], Ramamurthy et al. [14], Ojha and Subbaiah [12] and Hussain et al. [8]. Hussain et al. [7] carried out an experimental study on side circular orifice and highlighted a discharge equation. Other than side slot or side orifice, side sluice gate and side weir are used to divert the flow from main channel to a secondary channel. Studies on such devices are extensively reported in literature [13], [1], [9], [5], [15].
Ramamurthy et al. [14] derived an expression for the flow through a rectangular side orifice discharging from a rectangular channel. Fig. 1 shows a typical sketch of the side orifice in an open channel. They considered the velocity of jet Vj issuing out from the orifice as resultant of the velocity in the channel V1 and velocity normal to the channel due to static head H and expressed discharge through orifice aswhere ; ; and
Here H1 is the head above the lower crest of the orifice; H2 is the head above the upper crest of the orifice; Cd is the coefficient of discharge; L is the width of the rectangular orifice; b is the height of the rectangular orifice; Ym is the depth of flow in the main channel; g is the acceleration due to gravity and W is sill height. They used the following equation for the coefficient of discharge [3]:where velocity ratioand
where B is the width of the channel.
Using Eqs. 1–4, they derived the following relation for the discharge through the orifice:whereandConsidering that the velocity of the upper layers will be higher than mean velocity V1, Ramamurthy et al. [14] introduced a flow reduction factor 0.95 in discharge computation which partly accounts for the effect of non-uniform velocity distribution,
The assumptions made in deriving the above discharge equation were that the channel is horizontal and the flow is subcritical. The validity of Eq. (8) was checked by [8] using experimental data collected on square side orifices of size L=0.044 m, 0.089 m and 0.133 m in an open channel of 9.15 m length, 0.50 m width and 0.60 m depth. The crest heights of the orifices were at 0.5, 0.10, 0.15 and 0.20 m. They have used ultrasonic flow meter for the calibration of weir used for measuring discharge from the side orifice and main channel. They reported that the Ramamurthy et al. [14] equation underestimates the discharge as shown in Fig. 2. This could be due to erroneous formulation of Eq. (1) where angle between the area and velocity vectors are not taken into consideration. The present paper deals with analytical consideration of discharge equation for the side orifices with due consideration of directions of velocity and area vector while computing the discharge i.e., .
Section snippets
Analytical consideration
Considering varying pressure head over the flow area of a lateral rectangular orifice of size L fitted in the side of an open channel at sill height W, discharge through the lateral orifice may be written asSubstitution of Eqs. (2), (3) into Eq. (10) yieldsAfter the integration of the terms on the right hand side of Eq. (11), it may be written as
Results and discussions
Generally, 70–80% of the total data are used for the calibration of an equation, and 20–30% for its validation [10], [8], [7], [11], [2], [6]. Hence Eq. (19) is validated using the remaining unused 20% data sets of Hussain et al. [8] for rectangular side orifices. Such validation is shown in Fig. 5, which depicts that the computed discharge is well within ±5% of the observed values. While the computed discharge from Ramamurthy et al. [14] equation for 20% unused data have more than 5% error as
Conclusions
A discharge equation for lateral orifices in open channel has been derived with due consideration of direction of velocity and area vectors and also polynomial variation of coefficient of discharge with velocity ratio. The derived discharge equation is checked for its accuracy using data of Hussain et al. [8] for rectangular orifices. The computed discharges using the proposed equation were within ±5% of the observed values while computed discharge from Ramamurthy et al. [14] equation has
References (15)
- et al.
Input determination for neural network models in water resources applications, Part 2 – case study: forecasting salinity in a river
J Hydrol Elsevier
(2005) - et al.
A discharge coefficient for a trapezoidal broad crested side weir in subcritical flow
J Flow Meas Instrum Elsevier
(2012) - et al.
Discharge characteristics of sharp-crested circular side orifices in open channels
J Flow Meas Instrum Elsevier
(2010) - et al.
Flow through sharp-crested rectangular side orifices under free flow condition in open channels
Agric Water Manag Elsevier
(2011) - et al.
Discharge coefficient of a semi-elliptical side weir in subcritical flow
J Flow Meas Instrum Elsevier
(2011) - et al.
Discharge Characteristics of a Trench Weir
Flow Meas Instrum Elsevier
(2010) - et al.
Discharge coefficient for sharp-crested side weir in subcritical flow
J Hydraul Eng
(1999)
Cited by (25)
Numerical simulation of the flow passing through the side weir-gate
2024, Flow Measurement and InstrumentationA hybrid ensemble machine learning model for discharge coefficient prediction of side orifices with different shapes
2023, Flow Measurement and InstrumentationNumerical simulation of free flow through side orifice in a circular open-channel using response surface method
2020, Flow Measurement and InstrumentationCitation Excerpt :They recommended a large orifice formulation, for which the small orifice formulation is a particular case. Hussain et al. [10] improved Ramamurthy et al. [1] equation to estimate the discharge coefficient of side rectangular orifice. Hussain et al. [6] proposed a new equation based on linear regression to estimate the discharge coefficient of side circular orifices in a rectangular channel.
Discharge equation for the gabion weir under through flow condition
2020, Flow Measurement and InstrumentationCitation Excerpt :The overflow flow lower limit is the flow profile when the free surface has reached just the downstream edge of the weir crest, while overflow flow occurs when the stream is flowing over the top of the weir. Hydraulics and flow characteristics over solid structures (such as normal broad and sharp-crested weir, side weir, sluice gate, side orifice, etc.) have widely been studied experimentally and numerically by various researchers [2–5]. Kells [6] investigated the spatially varied flow over rockfill embankments in two states i.e., partial overtopping and the full overtopping.
Analytical and experimental study of flow through elliptical side orifices
2020, Flow Measurement and InstrumentationCitation Excerpt :The discharge coefficient expressions proposed by Hussain et al. [9,10] are mainly depend on the upstream Froude number and ratio of the orifice size and the main channel width. Hussain et al. [11] estimated the flow discharge of a rectangular side orifice using analytical solutions and compared it with the experimental data of Hussain et al. [10]. They derived a discharge equation for rectangular side orifices in rectangular open channel with due consideration of velocity direction and area vectors and also polynomial variation of discharge coefficient with velocity ratio.
Application of NARX neural network model for discharge prediction through lateral orifices
2018, Alexandria Engineering JournalCitation Excerpt :They further recommended that the orifice can be considered as small. Hussain et al. [12] analytically derived a relationship to calculate the discharge through rectangular side orifices considering the varying pressure distribution over the flow area. They found out that the second order polynomial variation of coefficient of discharge with the velocity ratio is better than the six order polynomial variation suggested by Carbadalla [2] and Ramamurthy et al. [16].