Fig 1.
Schematics of a conventional pressure compensating online drip emitter which uses a flexible membrane to control flow rate.
A: Isometric view showing the section planes. B: Cross-sectional view on the A-A plane. C: MATLAB modeled schematic corresponding to the cut view on the A-A plane. D: MATLAB modeled schematic corresponding to the cut view on the B-B plane. C and D show the critical dimensions of the flow features within the emitter which were used to model its behavior.
Fig 2.
Graphical summary of the working principle of a drip emitter.
A and B: Bending of the flexible membrane shown in the A-A and B-B planes from Fig 1A, respectively. C and D: Line force contact between the membrane and the lands, shown in the A-A and B-B planes from Fig 1A, respectively. E and F: Deflection of the membrane into the channel from shearing, shown in the A-A and B-B planes from Fig 1A, respectively. The flow path of water is shown by the blue lines and arrows. The dashed blue lines signify fluid flow behind the objects in view. Gray arrows denote the pressure differential acting on the membrane. Bold arrows denote the contact force at the edge of the land, FLine. The black triangles show constraints to membrane deflection.
Fig 3.
Flow control performance of a PC drip emitter.
Solid line shows the generic behavior of a commercially available PC emitter [14], which was used as the benchmark in this study. The leftmost vertical dotted line shows the ‘activation pressure’, which is the minimum pressure required for the emitter to achieve its rated volumetric flow rate. The region marked ‘Range’ denotes the typical operation pressure range for the emitter. The horizontal dashed lines show acceptable tolerances for the rated volumetric flow rate.
Fig 4.
Fluid flow modeling through an 8 L/hr drip emitter.
A: Bending of the flexible membrane under initial loading, cut in the A-A plane shown in Fig 1A. The primary flow restriction in this case is caused by κorifice, shown by a resistor symbol and plotted in the first section of Fig 4D. B: Shearing of the flexible membrane into the channel, cut in the A-A plane shown in Fig 1. Flow restriction is caused by the sum of κorifice and the variable resistance (shown by the variable resistor symbol) of κchannel, which increases with rising inlet pressure as shown in Fig 4D. C: Flow rate versus inlet pressure for pressure compensating behavior. D: Loss coefficient in the fluid network versus inlet pressure.
Fig 5.
A: Cross-section schematic of a modified emitter used to measure the orifice loss coefficient. The bottom half of a conventional emitter (like that in Fig 1) was removed so the orifice was the only source of flow restriction. For this test, the compliant membrane was replaced by a solid membrane. B: Measured values of κorifice versus pressure, with an average of κorifice = 0.95.
Fig 6.
Iterative process used to model the coupled fluid-structure behavior within a drip emitter.
A. Block diagram of the solver. B. The flow rate is solved iteratively for each increment of inlet pressure. The vertical dashed lines correspond to input pressure steps in the model. The circles are iterative solutions to flow rate. The asterisks are the final solution of flow rate for each inlet pressure. This model results in the full pressure versus flow rate relationship for a emitter of given internal geometry and membrane material.
Table 1.
Calculated geometric changes in the channel and resulting friction factor with increasing pressure.
Fig 7.
Mechanics that yield pressure compensating behavior and a linear increase in the total loss coefficient.
Bending of the flexible membrane under loading, cut in the A-A plane from Fig 1A. Increases in inlet pressure cause the flexible membrane to deflect further and cover up a larger length of the channel. This results in an increase in effective length of the flow path. As the membrane shears further into the channel with increasing input pressure, the cross sectional area and hydraulic diameter of the channel are decreased.
Fig 8.
Experimental setup used to test drip emitters.
The inlet pressure of water connected to the emitters is controlled by a pressure regulating valve. Flow rate was determined by measuring the time to fill 250 ml graduated cylinders. Two drip emitters could be tested simultaneously.
Table 2.
Error analysis on experimental measurements.
Table 3.
Dimensions for the nine emitters tested in this study.
Fig 9.
Flow rate versus inlet pressure for the JAIN emitter.
Blue scatter dots are data collected in this study, aggregated as box plots. Black dots are results reported by the manufacturer. Solid line is theoretical prediction.
Fig 10.
Flow rate versus inlet pressure for variations in channel length.
Blue scatter dots are data collected in this study, aggregated as box plots. Solid line is theoretical prediction.
Fig 11.
Flow rate versus inlet pressure with variations in channel depth.
Blue scatter dots are data collected in this study, aggregated as box plots. Solid line is theoretical prediction.
Fig 12.
Flow rate versus inlet pressure with variations in topology.
A: Variations in channel width; B: Variations in deflection to lands. Blue scatter dots are data collected in this study, aggregated as box plots. Solid line is theoretical prediction.
Fig 13.
Flow rate versus inlet pressure for emitters with multiple geometric variations.
A: Variations in both channel depth and max height of membrane deflection. B: Variations in both channel depth and channel width. Blue scatter dots are data collected in this study, aggregated as box plots. Solid line is theoretical prediction.