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GVSU EGR 365 - CONVERGING - DIVERGING CHANNEL

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CONVerging - diverging channelEGR 365 – FLUID MECHANICSPURPOSE:THEORY:APPARATUS:ITEMPROCEDURE:RESULTS:ANALYSIS:CONCLUSION:Grand Valley State UniversityThe Padnos School of EngineeringCONVERGING - DIVERGING CHANNELEGR 365 – FLUID MECHANICSBrad Vander Veen June 3, 2003Lab PartnersJulie WatjerPURPOSE:The purpose of this lab is to measure the static pressure variation through an enclosed converging-diverging channel (nozzle) at a given flow rate, and to compare those measurements to the predictions obtained from Bernoulli’s equations. Based on these results, regions of flow in which Bernoulli’s equation can and cannot be applied will be identified.THEORY:Consider the diagram of the flow area and pitot static tube below in Figure 1:Figure 1 – Diagram of Flow Area and Pitot Static TubeWriting Bernoulli’s equation at any two points (1) and (2) yields:tsspvpvp 2222112121 (1)-where ps is the static pressure, v is the velocity, and pt is the total pressureKnowing conservation of mass to be true:2211AvAv  (2)-where v is the velocity, and A is the cross-sectional area.Combining these two equations gives us a measure of pressure in non-dimensional form:212221222112115.0 AAvvvpp (3)-where p1, v1, and A1 are properties at the throat, and p2, v2, and A2, are all properties at some other point in the flow, and  is the density of the fluid.In this experiment, a pitot static tube will be used for measuring the dynamic head, whichis:25.0 vppst (4)Combining Equation (3) and (4) yields:212211121AAppppstss (5)APPARATUS:ITEM Airflow Bench Pitot Static Tube ManometerMeterstickPROCEDURE:1). Assemble the experimental setup as seen in Figure 1.2). Measure the depth of the flow channel3). Turn on the Airflow Bench.4). Start at the top, and move down at increments of 1cm until the bottom is reached. At each distance, conduct the following:a) measure the width of the channelb) record static pressure using the manometerc) record total pressure using the manometerRESULTS:distance from top [m] width [m] area [m^2]static pressure[mbar]total pressure[mbar] 0 0.075 0.00360 11.4 15.60.01 0.07 0.00336 10.8 15.60.02 0.065 0.00312 9.8 15.60.03 0.061 0.00293 9.2 15.60.04 0.056 0.00269 8.2 15.60.05 0.052 0.00250 7 15.60.06 0.047 0.00226 5.6 15.60.07 0.044 0.00211 4.4 15.60.08 0.044 0.00211 3.8 15.80.09 0.044 0.00211 3.4 15.80.1 0.044 0.00211 3.4 15.80.11 0.044 0.00211 3.4 15.80.12 0.045 0.00216 3.6 15.80.13 0.046 0.00221 4 15.80.14 0.048 0.00230 4.6 15.80.15 0.05 0.00240 5.2 15.80.16 0.052 0.00250 5.6 15.80.17 0.054 0.00259 6 15.80.18 0.056 0.00269 6.6 15.80.19 0.057 0.00274 7 15.80.2 0.058 0.00278 7.4 15.60.21 0.06 0.00288 7.6 15.60.22 0.061 0.00293 8 15.60.23 0.063 0.00302 8.2 15.60.24 0.065 0.00312 8.4 15.60.25 0.066 0.00317 8.6 15.60.26 0.068 0.00326 8.8 15.60.27 0.07 0.00336 9 15.60.28 0.071 0.00341 9.2 15.60.29 0.072 0.00346 9.4 15.60.3 0.074 0.00355 9.6 15.6Table 2 – Recorded Results (throat in yellow)ANALYSIS:In Figure 3 below, the experimental normalized pressure is plotted versus the known cross-sectional area ratio. On the same plot, the theoretical values for normalized pressure are plotted. The experimental normalized pressure was calculated using the left side of Equation (5) while the theoretical was calculated using the right side.Normalized Pressure vs. Area Ratio0.0000.1000.2000.3000.4000.5000.6000.7000.59 0.72 0.94 1.00 0.98 0.88 0.79 0.73 0.68 0.63 0.59A1 / A2Normalized PressureTheoreticalActualFigure 4 – Plot of Theoretical Normalized Pressure vs. Actual Normalized PressureNote that before the throat, the theoretical normalized pressure seems to match the actual normalized pressure quite well. However, after the throat, the two sets seem to diverge from each other. This can be explained because the theoretical values do not assume any losses throughout the flow channel. As measurements were taken at points further down in the flow channel, the losses accumulated, and were very apparent in the results. Even though the beginning and end of the channel had the same area, the pressure at the end did not return to where it started. This was due to the losses.In Figure 5 below, the dimensional parameters of the flow can be seen.Pressure vs. Area0246810121416180.0036 0.0029 0.0023 0.0021 0.0022 0.0024 0.0027 0.0029 0.0031 0.0034 0.0036Area (m ^2)Pressure (mbar)P_tP_sFigure 5 – Actual Pressure vs. Cross Sectional AreaThe velocity of the fluid in the channel can also be plotted as seen below in Figure 6. These velocity values were calculated using Equation (4) Air Speed vs. Area20.0025.0030.0035.0040.0045.0050.000.0036 0.0027 0.0021 0.0022 0.0025 0.0028 0.0031 0.0034Area (m ^2)Air Speed (m /s)Air SpeedFigure 6 – Air Speed vs. Cross Sectional AreaCONCLUSION:In this lab, measurements of pressure were taken throughout a flow channel. Theoretical data showed that in areas where the channel narrowed, the static pressure would decrease and the fluid velocity would increase. These predictions were confirmed by actual resultsfound in this lab. Also discovered in this lab was that Bernoulli’s equation holds well for flow through a channel before in converges, but after the channel diverges, the losses are significant and Bernoulli’s equation becomes


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