Grand Valley State University The Padnos School of Engineering MINOR LOSSES EGR 365 FLUID MECHANICS Brad Vander Veen July 15 2003 Lab Partners Julie Watjer PURPOSE To experimentally determine minor losses through a rounded exit and through a fullyopen globe valve THEORY Consider the diagram of the experimental setup below in Figure 1 Figure 1 Experimental Setup Consider a large hollow cylinder filled with water If a small opening is placed on the bottom of the cylinder the fluid will flow out By placing valves and fittings in this opening the flow can be controlled In this lab the loss coefficients of a rounded exit and a globe valve will be analyzed Now consider the steady state energy equation p p1 1 2 2 Q W m 2 v 2 v1 g z 2 z1 losses 2 1 where Q is the heat transfer W is work added to the system p is the pressure v is the velocity g is gravitational acceleration z is the height and the losses are major and minor losses In this lab major losses will be neglected because the viscous effects of the water flowing through the cylinder are minimal The minor losses are defined as v2 losses k 2 2 where k is the loss coefficient and v is the velocity Using Equations 1 and 2 the height of the water can be found A0 1 2 1 2 g t h0 At h t 2 1 2 2 1 k 2 A0 At 2 3 where h t is the height of the water at any time t h0 is the initial height A0 is the cross sectional area of the outlet At is the cross sectional area of the tank g is gravitational acceleration and k is the loss coefficient Solving for the losses coefficient k 1 A0 2 AT h0 1 2 2 2 gt 2 A0 1 h1 2 2 At 4 where h0 is the initial height A0 is the cross sectional area of the outlet At is the cross sectional area of the tank g is gravitational acceleration t is the change in time and k is the loss coefficient APPARATUS ITEM Water tank Globe Valve Meterstick Stopwatch 5 8 rounded washer PROCEDURE 1 Place the rounded washer in the opening in the bottom of the tank 2 Fill the tank with water 3 Measure the height of the water every 3 from the bottom up to 45 4 Allow the water to run out and record the time when the water height reaches each increment of 3 5 Attached the globe valve to the bottom of the tank and repeat steps 1 4 RESULTS In Table 2 below the results of the procedure can be seen height in time with washer s time with washer and valve s 45 42 39 36 33 30 27 24 21 18 15 12 9 6 3 0 0 5 4 10 1 17 22 3 28 7 35 2 43 7 53 4 63 75 86 101 118 140 190 0 15 5 31 46 62 80 88 116 144 157 180 204 230 260 293 337 Table 2 Experiment Results In Figure 3 below a plot of the water height using only the washer can be seen Height vs Tim e 50 45 Height vs Time 40 35 30 25 20 15 10 5 0 0 50 100 150 200 time s Figure 3 Height vs Time In Figure 4 below a plot of the water height using the washer and valve can be seen Height vs Tim e 50 45 Height vs Time 40 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 time s Figure 4 Height vs Time 350 400 ANALYSIS Using Equation 4 from the theory section between each two data points on each of the curves yields a losses coefficient calculation for each curve The k values can be seen below in Table 5 height in k washer only k washer and valve 45 42 39 36 33 30 27 24 21 18 15 12 9 6 3 0 0 366907366 0 035960431 0 923738064 0 044138583 0 390002216 0 297066321 0 984230317 1 279462751 0 934298501 1 555853461 0 75534731 1 533544318 1 312806849 1 280593401 1 021116961 10 26189454 9 484733713 8 091342942 8 515721472 9 995047973 0 964780391 20 53117832 17 99341201 2 547042992 8 38917811 7 355986272 6 611867987 6 202486137 4 13131946 0 565155807 Table 5 K values for each curve By taking the average of each set of data a total loss coefficient is found k for washer only 0 843 k or washer and globe valve 8 109 By subtracting the k value due to the washer from the k value of washer and globe valve the k value of the globe valve only can be found k for globe valve only 7 266 ERROR The formula for the propagated error in this lab is 2 2 U 5 error t 04 12 t Note that since the k value for the globe valve was found using the k value for the exit the error on the k value for the globe is twice the error for the exit DISCUSSION As can be seen from the data the losses due to the rounded washer at the exit are very minimal This is because the water flows very easily through this orifice without much disturbance If the washer were not rounded the losses would be much greater The globe valve adds a significant loss to the flow This is because of the geometric characteristics of the globe valve The water must actually go through a jog because of the shape of the globe valve and this causes a tremendous loss in the flow A valve that would assume the same function would be a simple gate valve but would have significantly fewer losses than the globe valve The accepted value of the loss coefficient for a rounded opening is 0 25 This yields a percent discrepancy of 230 The accepted value of the loss coefficient for the globe valve used is 14 This yields a percent discrepancy of 48 CONCLUSION In this lab tests were conducted to experimentally measure the k value for a simple rounded washer at an exit and the k value for a fully open globe valve The k value for the rounded washer was 0 843 0 04 and the k value for the fully open gate valve was 7 266 0 08