Venturi Apparatus - des fluides...Venturi Apparatus 2 Table of Contents ... Theory An incompressible...

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  • Venturi ApparatusME-8598

    Instruct ion Manual012-09486B

    *012-09486*

  • Ventur i Apparatus

    2

    Table of Contents

    Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Pre-Setup Measurements 4Setup 5Procedure 5Analysis 5Further Analysis 6Clean-up 6Storage 6

    Appendix A: Quad Pressure Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7DataStudio 7Xplorer GLX (Standalone Mode) 7

    Appendix B: Fluid Supply and Flow Rate Measurement Options . . . . . . . . . . . . . . . . . . 8Air 8Water 10

    Appendix C: Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    Material Safety Data Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

  • Venturi ApparatusME-8598

    3

    Included Equipment Part Number Air Method: Recommended Equipment 1 Part Number

    1. Venturi Apparatus base and top plate ME-8598 Spirometer Sensor 2 PS-2152

    2. T-knob Screws (qty. 8) 617-024 One of the following:

    3. Spirometer Tubing, 2.5 cm ID, 15 cm long 640-053 Shop Vacuum (or similar air supply) 3

    4. Rubber Stoppers, 1-hole (qty. 2) 648-09597 Balloon and balloon pump

    5. Restriction Clamps (qty. 2) 640-052 Water Method: Recommended Equipment 4

    6. Fluid Tubing, 6 mm ID, 6 m long 640-012 Water Reservoir (or similar container) ME-8594

    Required Equipment Container to catch water

    Quad Pressure Sensor PS-2164 Table Clamp ME-9472

    PASPORT Interface 5 See PASCO catalog or www.pasco.com

    120 cm rod ME-8741

    2 Three-finger clamps SE-9445

    One of the following:

    Motion Sensor 2 PS-2103

    Rotary Motion Sensor 2 PS-2120

    Force Sensor 2 PS-2104

    Stopwatch SE-8702B

    1See page 8 for more information.2The use of this sensor and the Quad Pressure Sensor simultaneously requires a multi-port PASPORT Interface (such as Xplorer GLX or PowerLink) or two single-port interfaces.3See pages 810 for more information.4See pages 1013 for more information.5PASPORT interfaces include Xplorer GLX (PS-2002), PowerLink (PS-2001), AirLink (PS-2005), Xplorer (PS-2000), and USB Link (PS-2100)

  • Ventur i Apparatus 012-09486B Introduct ion

    4

    Introduction

    In the Venturi Apparatus, air or water flows through a channel of varying width. As the cross-sectional area changes, volumetric flow rate remains constant, but the veloc-ity and pressure of the fluid vary. With a Quad Pressure Sensor connected to the built-in Pitot tubes, the Venturi Apparatus allows the quantitative study and verifica-tion of the Continuity Equation, Bernoullis principle, and the Venturi effect.

    The model ME-8598 Venturi Apparatus includes the connectors and tubing needed for doing the experiment with either air or water. This manual contains complete experiment instructions, including several options for fluid supply and flow-rate mea-surement.

    Theory

    An incompressible fluid of density flows through a pipe of vary-ing diameter (see Figure 1). As the cross-sectional area decreases from A0 (large) to A (small), the speed of the fluid increases from 0 to .

    The flow rate, R, (volume/time) of the fluid through the tube is related to the speed of the fluid (distance/time) and the cross-sec-tional area of the pipe. The flow rate must be constant over the length of the pipe. This relationship is known as the Continuity Equation, and can be expressed as

    (eq. 1) R = A00 = A

    As the fluid travels from the wide part of the pipe to the constriction, the speed increases from 0 to , and the pressure decreases from P0 to P. If the pressure change is due only to the velocity change, Bernoulli's Equation can be simplified to:

    (eq. 2)

    Experiment

    This experiment can be conducted with either air or water. Appendix B contains equipment lists and instructions specific to each method.

    Note: You can use a PASPORT interface (or interfaces) connected to a computer running DataStudio software or on an Xplorer GLX interface in standalone mode (without a computer). For instructions on collecting, graphing, and analyzing data, press F1 to open DataStudio on-line help, or see the Xplorer GLX Users Guide.

    Pre-Setup Measurements

    Remove the top plate from the apparatus. Measure the depth of the channel and the widths of the wide and narrow sections. Calculate the largest cross-sectional area (AL) and the smallest cross-sectional area (AS).

    Figure 1: Fluid flow through a pipe of varying diameter

    P P012--- 2 0

    2( )=

  • Model No. ME-8598 Exper iment

    5

    Setup

    1. Connect the Quad Pressure Sensor to your PASPORT interface (but do not connect tubing to the pressure ports yet). If you are using a com-puter, start DataStudio.

    2. Calibrate the Quad Pressure Sensor (see Appendix A).

    3. Connect each of the four pres-sure tubes extending from the underside of the apparatus to the ports of the Quad Pressure Sensor as indicated in Figure 2.

    Important: Do not allow water to enter the sensor. Ensure that there is no water near the sensor end of the pres-sure tubes.

    4. Place the top plate on the apparatus and secure it with eight T-knob screws. Tighten the screws no more than necessary to prevent leaking.

    5. Set up the fluid supply and flow-rate measurement as described in Appendix B.

    Procedure

    1. Start fluid flow.

    2. Start data collection on the computer or interface.

    3. Continue data collection while observing the pressure measurements on a graph display. Obtain a few seconds worth of good data before stopping data collection and fluid flow.

    Analysis

    1. View your data on a graph of pressure versus time.

    2. Select a time interval of about 2 seconds in which all off the pressure measure-ments are relatively clean (though not necessarily constant or noise-free).

    3. Within this time interval, determine the average of each pressure measurement: P1, P2, P3 (and P4 if you will do the Further Analysis below).

    4. Over the same 2-second interval, determine the average flow rate, R.

    5. If there were no friction or turbulence in the channel, the pressures in both wide sections (P1 and P3) would be equal; however, you will find that this is not the case. Because the channel is symmetrical about Point 2, you can estimate the pressure lost at Point 2 due to friction and turbulence by assuming that it is half of the pressure lost between Point 1 and Point 3. In other words, if the tube were

    Figure 2: Quad Pressure Sensor connected to apparatus

  • Ventur i Apparatus 012-09486B Exper iment

    6

    straight, the pressure at Point 2 would be the average of P1 and P3. Calculate this theoretical pressure:

    (eq. 3)

    6. Use the measured flow rate, R, and Equation 1 to calculate the fluid speed in the wide parts of the tube (0), and the speed in the venturi constriction ().

    7. Use these values of 0 and and Equation 2 to calculate the theoretical pressure (P) in the venturi constriction. Compare this to the actual pressure measured by the sensor (P2).

    Further Analysis

    Repeat the analysis above for Points 2, 3, and 4.

    Clean-up

    1. Allow the water reservoir to run empty. Tilt the apparatus to empty water from it.

    2. With the apparatus empty of water, disconnect the pressure tubes from the sensor. (Leave the tubes connected to the underside of the apparatus.)

    3. Remove the top plate from the apparatus. Allow the apparatus and tubing to dry completely.

    Storage

    Store the apparatus with the top plate loose to avoid permanently deforming the seal.

    P0P1 P2+

    2------------------=

  • Model No. ME-8598 Appendix A: Quad Pressure Cal ibrat ion

    7

    Appendix A: Quad Pressure Calibration

    The purpose of this calibration is to fine-tune all four pressure measurements so they read the same when exposed to the atmosphere. This will allow the small pressure dif-ferences that occur in the apparatus to be measured more accurately.

    Conduct this procedure with all four pressure ports exposed to the same pressure.

    DataStudio

    1. Click the Setup button to open the Experiment Setup win-dow.

    2. Click the Calibrate Sensors button to open the calibration window (see Figure 3).

    3. At the top of the Calibrate Sensors window, select Quad Pressure Sensor.

    4. Select the Calibrate all similar measurements simulta-neously option.

    5. Select the 1 Point (Adjust Offset Only) option.

    6. Click Read From Sensor (in the Calibration Point 1 section of the window).

    7. Click OK.

    Xplorer GLX (Standalone Mode)

    1. Press + to open the Sensors Screen.

    2. Press again to open the Sensors menu.

    3. From the menu, select Calibrate to open the Calibrate Sensors win-dow (see Figure 4).

    4. In the first box of the window, select Quad Pressure Sensor.

    5. In the third box of the window, select Calibrate All Similar Mea-surements.

    6. In the Calibration Type box, select 1 Point Offset.

    7. Press (Read Pt 1).

    8. Press (OK).