Many high school and introductory college physics courses cover topics in fluidics through the Bernoulli and Poiseuille equations, and consequently one might think that siphons should present an excellent opportunity to engage students in various laboratory measurement exercises incorporating these fascinating devices. However, the flow rates (or average exit velocities) of simple water siphons have not been sufficiently explained,1 nor has an associated analytical model been developed demonstrating sufficient experimental correspondence to allow physics instructors to bring closure between theoretical concepts and laboratory experiences. We present such an explanation and analytical model for the flow rates of simple water tube siphons. Further, we report measurements that show the model gives good correspondence to flow rates of siphons over a wide range of tube lengths, inner diameters, and water heights (hydrostatic head), and for which the Reynolds numbers range from 102 to 105.

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12.
Note that for an entrance constriction of 0.5, fluid element acceleration does not occur along the centerline at the entrance, compared to a constriction coefficient of 1.0, where the velocity along the centerline doubles. We speculate that this results in a reduction of the entrance lengths, and further likely accounts for a delaying (in terms of Reynolds number) in the onset of turbulence along the remainder of the tube, relative to bell- or trumpet-shaped tube entrances exiting the side of a tank.
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