Flow Rate vs. Headloss for Variable Tube Lengths

Abstract

Using the new flow control apparatus, flow rates were calculated relative to head loss and plotted against the Hagen-Poiseuille equation to analyze divergence from the mathematical model and provide an idea of how the application of equations should be affected to provide a better model for reality.

Introduction and Objectives

The problem of dosing is an important one that composes part of the corner stone for the entirety of the plant. Dosing with chlorine and alum are critical for purification of relatively clean water and the flocculation process. However, due to the inability of the equation to properly model the dosing process, head losses which should produce certain flow rates produce substantially lower flow rates. This experiment will quantify the deviation of flow rate data collected from the expected results as calculated by the Hagen-Poiseuille equation.

Procedures

The tested apparatus was constructed as explained on the previous page. Since it has been determined that the water level in the constant head tank is affected by the water level in the stock tank, before each iteration of the experiment, the water collected from the previous test is replaced to keep the water constant. Data is collected via the EasyData program which collects voltage output for a 7 kPa sensor.

At first, increments of 25 mL were placed over the sensor, to obtain a direct conversion value between voltage and volume of water. This allowed for a direct change of voltage to volume and thus a simpler calculation of flow rate through the tube.

After this conversion value was determined, the flow rate test was commenced. After the constant head tank was filled and the stock tank was prepared, the distribution tube was placed in a hole on the apparatus such that a known head loss was induced. Using Easy Data, a plot of voltage vs time was constructed. Transforming voltage to volume produced volume vs time. The derivative of this graph is the flow rate out of the dosing tube. The procedure was varied using differing head losses and different tubing lengths.

Results and discussion

The test was run for two different tube lengths, 1 m and 44.5 cm. The test was run at many different flow rates from head loss of 3 cm to 25 cm. The plants in Honduras induce, at the most, a head loss of 20cm. The test was meant to also allow for an end behavior analysis for over dosing.

Conclusions

This experiment confirmed that the Hagen-Poiseuille equation overestimated the actual flow rate and thus was providing an inaccurate estimate. However, the extent of this over/under estimation was previously difficult to determine. However, what is most interesting is the validity of the supposed correction. Using the values calculated from the experiments regarding the tube diameter provided a drastic improvement which may be a correction that could be the correct calculation. Also, because the inner diameter of the tube was 1/8th of an inch, small variation in inner diameter produce large changes in the data. Varying tube diameters should be tested to find if these minor variations are negligible at larger diameters. Varying tube lengths should be tested to consider the possibility of non-negligible minor head losses which, when considered, provide better fits to the calculated graphs.