Physics 6268, Group 5: Chaotic Dripping Faucet

The dripping faucet experiment seeks to provide a relatively simple visualization of a system that exhibits seemingly predictable dynamics that quickly transitions to an entirely unpredictable, chaotic behavior under certain conditions. This behavior is first modeled through equations determine from previosu research and papers in order to understand the general phenomenon and established a baseline to comapre results against. Through a straightforward experimental setup, the time between drips of a faucet is measured using a photodiode and a laser. The number of drips are dictated through precise control of flow rate through a flow regulator. The photodiode records this drop as the water drop temporarily diffracts the laser path to the diode. The photodiode is interfaced to a computer through an analog to digital converter. The data is easily analyzed and visualized through the computer. After conducting error analysis, the processed data was examined in MATLAB and analyzed.The lessons learned through this research should include fine attention to detail regarding the experimental setup. It is imperative to have accurate flow control and uniform flow rate. It is suggested that shunting the flow to allow finer resolution of the water passing through the nozzle, while still using the crude units of the pump, be performed in order to increase the flow rate resolution. This would allow finer investigation of the 70-90 flow-rate unit (FRU) region of the pump, where the period doubling and chaotic behavior seemed to be most apparent. Furthermore, large nozzle size is important to minimize imperfections and allow harmonic oscillator dynamics. For data collection, care must be taken to exclude satellite drops and debounce the laser-photodiode to remove the double crossings generated by falling drops. The results show two main regimes: a period doubling regime, and a chaotic regime. The system gradually transitions from a single period to double period, followed by four periods. Once the flow rate is increased past these period doubling regimes, the time between drips becomes apparently unpredictable. Plotting the current