Application of gated conduits for fertigation in irrigation systems

A_w

water flow cross-sectional area

B

water surface width

D

conduit diameter

Fr

Froude number based on effective depth in conduit

g

gravitational acceleration

h

gate opening

y_e

effective depth

L

conduit length

Q_F

fluid flow rate in suction pipe

Q_F/Q_W

fluid-injection ratio (ratio of fluid flow rate to that of water)

Q_W

water flow rate in conduit

V_W

water flow velocity at gate location

μ

dynamic viscosity

γ

density

φ

ratio of water cross-sectional flow area to conduit cross-sectional area

Gated conduits ensure that water is transferred downstream from the reservoir, to facilitate lowering of the reservoir level and/or to ensure maintenance of the biological minimum flow required downstream. For small dams and reservoirs, gated conduits often also serve as water intakes for some users, mostly for irrigation (Tanchev 2014).

Gated conduits are hydraulic structures that involve high-velocity air-water flow. If the conduit gate is opened partially, flow velocity increases due to the reduced cross-section. High-velocity flow can cause structural damage, e.g., by cavitation. To reduce or eliminate this damage, a suction pipe is installed after the gate, where flow velocity is high, so that air is drawn into the conduit and the pressure downstream of the gate is maintained at a safe level.

Numerous studies have been reported concerning air-injection ratios in gated conduits, e.g., Aydin et al. (2021), Baylar et al. (2021, 2022); Hohermuth (2019), Hohermuth et al. (2020), Pengchengi et al. (2022). The study results, between them, show that the air-injection ratio is a function of geometry and hydraulics.

Fluid injection created in gated conduits can be used for many purposes such as solving environmental problems such as lack of dissolved oxygen (Baylar et al. 2010). They can also be used to inject liquid fertilizers or chemicals into pressurized irrigation systems, as investigated in this study.

When a conduit cross-section is partially closed by a gate, high-velocity and low-pressure flow occurs downstream of the gate, and pressure below atmospheric can occur within the conduit. Theoretically, these pressures could be as low as the vapor pressure of water. When an atmospheric connection is made by installing a suction pipe after the gate, fluid suction occurs in the suction pipe (Figure 1). The extent of fluid suction inside varies according to the flow's entraining and carrying capacity. The pressure reduction downstream of the gate is a function of the Froude number (Fr), gate opening proportion and conduit length, and the fluid's density and viscosity.

The aim of the study was to understand the role of the gated conduit in the fluid-injection ratio. The experimental setup was built at Firat University Hydraulic Laboratory, Elazig, Turkey, and the components used are shown in Figure 2.

The gated conduit's fluid-injection ratio was investigated using fluids with different densities and viscosities – see Table 1. The oil used in the tests was used engine oil.

Gate opening proportions (φ) of 15, 30 and 60% of the conduit's cross-section were used (Figure 3) and water was passed at different flow rates (Q_W) under the gate. An electromagnetic flow meter was used to measure the flow rate. The conduit diameter (D) was 68 mm, and three conduit lengths (L) were used: 2, 4, and 6 m.

The first injection fluid studied was air, the velocity of which was measured in suction pipes at four locations downstream of the gate with an anemometer (Testo Model 435). The anemometer was placed in the middle of the suction pipe and each measurement lasted for at least 60 seconds. The accuracy of the anemometer used is ±0.2 m/s +1.5% of mv. Precautions were taken to ensure that the anemometer was always perpendicular to the direction of airflow. The fluid-injection ratios for oil and water were measured by delivering them into the system from a graduated container. Thus, after water passed through the conduit, the ends of the suction pipes were immersed in the graduated container for a measured time – about 20 seconds – and the volume change in the graduated container measured, so that the flow rate could be determined. The list of experiments is given in Table 2.

The variation of the fluid-injection ratio (Q_F/Q_W) with Fr for φ and L is shown in Figures 5 and 6. As can be seen, Q_F/Q_W increased as Fr increased in all experiments. In other words, there is a direct relationship between Fr and Q_F/Q_W.

Q_F/Q_W decreased with increasing φ because the pressure difference between the upstream and downstream sides of the gate decreases as the gate's open proportion increases. Q_F/Q_W also decreased with increasing L, because the pressure difference between the upstream and downstream sides of the gate also decreases as L increases.

Figures 5 and 6 show that the best Q_F/Q_W value was achieved in the gated conduit with φ = 15% and L = 2 m. The Q_F/Q_W values of all three fluids were, therefore, compared for φ = 15% and L = 2 m. Figure 7 shows plots of Q_F/Q_W vs Fr for all three fluids. As can be seen, Q_F/Q_W increases with increasing Fr in every case.

Fluid density (γ) is also an important parameter affecting Q_F/Q_W. It was observed that more air was injected than either water or oil. However, water's Q_F/Q_W exceeded that of oil, even though its density was higher, because its viscosity (μ) is lower.

Fluid viscosity is also an important influence on Q_F/Q_W, which increases with decreasing fluid viscosity, making it easier to inject the fluid into the system.

In this study, the fluid-injection ratio of gated conduits was examined. When a gate is partially opened, the water flow velocity under it increases due to the reduced cross-section. As the flow velocity increases, the pressure downstream of the gate decreases, because of which fluid can be drawn into the conduit via a suction pipe opened downstream of the gate. Numerous field measurements and model studies were carried out to determine the air-injection ratio in the gated conduits, but extensive literature searches have not shown any published analytical or physical studies of the fluid-injection ratio in gated conduits. Laboratory experiments were done, therefore, to determine the fluid-injection ratio of gated conduits, from which it was concluded that:

• Gated conduits have a high fluid-injection ratio.

• The fluid-injection ratio increases as the Froude number increases as well as when the gate opening proportion decreases, but decreases with increasing conduit length.

• Fluid density affects the fluid-injection ratio, as does fluid viscosity – the fluid-injection ratio increasing with decreasing fluid viscosity.

We would like to thank the editor and the reviewers for taking the time and effort necessary to review the manuscript. We sincerely appreciate all valuable comments and suggestions, which helped us to improve the quality of the manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.