An exercise combining theoretical calculation and experimental measurement of hydraulic losses in gravity-driven pipe flow provides a versatile and economical learning platform for mechanical engineering technology students. The exercise is utilized in a junior level course in thermal and fluids engineering in order to reinforce lecture material on viscous incompressible flows. The example studied essentially simulates the flow from a water tower in miniature. It involves the gravity-driven flow of water through a length of tubing in which a constant head differential is maintained between the entrance and exit of the tubing using a reservoir with the water maintained at a constant depth. Typically, the flow falls in the turbulent regime with hydraulically smooth pipe walls. The theoretical component involves modeling the system using the incompressible flow energy equation, with analytical calculation of the head losses. Incorporating such loss components as Reynolds number dependent skin friction, results in an equation for the flow rate that needs to be solved iteratively. The iterative solution is easily carried out in a spread sheet. Computing the solution in a spread sheet gives students valuable experience in performing flow modeling of a type that is often useful in industry. The experimental component provides ample opportunities for students to gain experience with pre-test uncertainty estimation, formulating and executing a test plan, and with post-test statistical analysis of experimentally derived flow parameters. As an example, flow rate is determined by measuring the time it takes to collect a measured volume of water discharged from the tubing. Each of the two variables, volume and time, are prone to sources of experimental uncertainty that are easily visualized by the students. Such tangible examples go a long way in helping students to understand techniques like the Kline-McClintock method for uncertainty estimation. The experimental apparatus is made up of inexpensive items found in home improvement stores, such as small diameter polyethylene tubing used in home ice makers, tube fittings, a plastic bucket for the feed reservoir, measuring vessels, and stopwatches. Typical head differentials involved are about 1 meter, and with the tubing sizes used, the flow rates are less than 2 liters/min. The quantities of water used are small, meaning that the testing can be carried out in almost any available instructional space. On account of the simplicity of the apparatus and test procedure, it is practical to vary parameters like reservoir height and tubing length. Sources of minor losses such as elbows and flow restrictions can also be introduced. Measurements can be repeated quickly, thereby facilitating the gathering of enough data to carry out a meaningful post-test statistical analysis. Comparison of theoretical and experimental results helps students gain insight into the advantages and limitations of both approaches.
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