[SOLUTION] Control Volume Methods

Control Volume Methods Purpose:The purpose of this lab is to gain hands-on experience using control volume methods to analyze systems of general and engineering interest.Introduction:Control volume methods provide powerful tools to gain “big-picture” information about various engineering systems without knowing much about the actual complicated flow patterns within the system.In this lab, you will do two experiments. In Experiment A, you will explore a fairly complex pump / turbine system and use the mechanical energy balance equation along with various physical measurements to approximate losses in the system. You will also determine the overall system efficiency. In Experiment B, you will consider a simple falling liquid jet and apply the integral form of conservation of mass to explain the observed shape of the jet.Include all of your work as an appendix after the “Literature Cited” section in your report.Experiment A: Efficiency of a Pump/Turbine SystemMaterials:· Pump and Liquid Turbine Apparatus· Ruler· Tape MeasureGiven measurements:· Inner diameter of steel pipe: 1.375 in· Height for Control Surface 2: 19.75 inProcedure:1. Fill the top and bottom tanks high enough that water is just above the base of the weir triangle that connects the tanks. When doing this, make sure that the plug between the upper and lower reservoirs is not inserted into the drain.2. Make sure the tank has a water level matching zero on the flowrate indicator located on the side of the tank.3. Ensure the valve between the pump and turbine is open. Do this by turning the valve four complete counter-clockwise turns (use the blue tape for reference).4. Insert the plug between the upper and lower reservoirs.5. Carefully have a group member walk behind the apparatus and quickly turn the black power dial from “0” to the “3” setting. This is low speed.6. Turn the valve clockwise until the valve is fully closed. The blue tape should be pointing toward the Bourdon gage.7. Turn the valve two full revolutions counter-clockwise (cc).8. Wait at least 15 seconds for the system to reach a steady-state.9. Record the gage pressure head (ft), the flowrate Q (L/s), and the height (in) from the bottom of the lower chamber of the tank to its free surface.10. Repeat Steps 5-8 three additional times, but now, turn the valve one half revolution for each iteration. At the end of this procedure, the valve should be at three and a half revolutions cc from the “closed” position.11. Turn the black power dial back to the “0” setting.12. Press the circular, red “Stop” button to shut off the pump.Report Results:· Assuming a constant rate of pump power input (W?P ? 0.5hp), determine an equation (in terms of known quantities) for the rate of mechanical energy lost (W ,1 ) in the section ofthe system stretching from the surface of the bottom reservoir, through the pump, through the piping, and up to the cross-section at the pressure gage.· In Excel or MATLAB, plot W ,1 vs Q using your recorded data and derived equation. Thisgraph should have labeled axes, a title, and a figure number (placed below the graph).· Assuming that the turbine extracts 60% of the mechanical energy input from the cross- section at the pressure gage (?T ? 0.6 ), determine an equation for the total rate of energyoutput by the turbine (WT ) and the overall efficiency of the system (?sys ? W?T W?P ).· In a second graph, plot ?sysvs Q. Once again, include all required labels.Report Discussion:· Comment on sources of error in this experiment.· List and explain all assumptions made to derive the equations used in your analysis. Were these assumptions valid throughout the experiment or only for certain aspects? Explain why or why not.· Comment on probable sources of head loss in the system. Which do you believe were the most substantial? Why?· Were your values of ?sys as expected? Why or why not?· What effect did opening and closing the valve have on the measured pressure, the flow rate, the rate of mechanical energy loss, and the overall system efficiency? Based on your analysis, why is this the case?