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The Point of failure experiment will evaluate the point at which the diameter of the LFOM is too small to accomodate the flow throuhg the riser pipe. At a certain point the water will back up in the pipe and then there won't be free flow from the orifice into the riser pipe. The small diameter riser pipe will be was tested at the pilot plant. The hypothesized results are a relationship taht is the same as the tearget realationship until failure and then a slope that is more vertical than the target line. The results showed a linear relationship that is more vertical with a lower ratio of flow/depth than the target values predicted for all flow rates. The hypothesis for these results is that instead of a point of failure there is total failure. If the pipe is inappropriately sized then the LFOM fails for all flow rates.
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In order to more accurately calcualte the optimal LFOM diameter it is necessary to know the point at which the diameter is to small and will achieve failure. The point of failure experiment will test a prototype design under predicted failure conditions. The point of failure is predicted assumeing a conservation of momentum.
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The entrance tank with riser pipe was installed in the plant and measurements were taken on the efficiency and accuracy of the design. There is an in-line flow meter that will provide flow rate data that can be compared to the flow rate recorded based on height in the entrance tank. There will be readings at incremental flow rates where the machine electronic flow meter flow rate and water height will be recorded.
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Correlation between Flow and Water Height
Differenece Between the Recorded Data and Predicted Values as a Function of Flow Rate
Percent Deviation Between the Recorded Data and the Predicted Values as a Function of Flow Rate
The linear trendline of the data is y = -0.9653x + 38.22, with an R^2 value of 0.9556. This allows us to calculate the flow rate where the error between the predicted and measured flow rates differ by more then 10%. The flow rate of failure is 49.95 L/min which is less than the expected flow rate of failure, 62.5 L/min.
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The results of the experiment were contrary to the expected results. Originally it was assumed that there was a certain maximum flow rate for a pipe, if the flow rate exceeded a maximum value the water entering the riser pipe wouldn't be able to leave quickly enough and the water would back - up in the pipe. THe results showed an alternative situation. The pipe was sized to reach the failure point at 62.5 L/min (half the maximum flow rate of the pilot plant - 125 L/min). The results showed a linear relationship between flow rate and height for all of the flow rates, the difference was that the slope for the pipe had a different slope than the predicted values. Therefore the hypothesized system reactions not entirely represent the actual situationThe lack of agreement between theory and experimental values over the entire range suggest that the LFOM failed over the entire range of flows.
Future Research
The perplexing results may be due to the fact that there we were not witnessing a point of failure, a flow rate at which a LFOM will fail, but a complete failure. If the pipe is sized too small to accomodate the flow rate which the orifice pattern is designed to support then the LFOM will fail for all flow rates. This hypothesis would agree with the results. It would be beneficial in future research to test the LFOM created above with a diameter of 1.5 inches with an orifice pattern designed to handle the maximum flow rate for the pipe, 62.5 L/min. It would also be interesting to apply a flow rate in excess of the 62.5 L/min and watch the system for evidence of failure.