Statics: Pressure Measurement

Transcription

1 Statics: Pressure Measurement Objectives In this laboratory, you will learn how to measure pressure using a computerized data acquisition system. You will build and test a bubbler system to measure the depth of water in a tank based on the relationship between pressure and depth of water. You will also take pressure measurements to determine the elevation of the distilled water storage tanks in Hollister Hall. Theory Pressure Transducers Pressure measurements were first made almost exclusively with manometers using mercury and water as the manometer fluids. The risk of mercury spills precludes the use of mercury. Pressure gages that create a deflection of a needle as pressure increases are also commonly used. With the advent of computerized data acquisition, sensors that can produce a voltage output that is related to a physical property are preferred. Pressure transducers produce a voltage output that is proportional to the applied pressure. Pressure transducers are available in gage, Figure 1-1. transducer. Differential pressure absolute, and differential configurations. The pressure transducers used in this experiment are differential and thus can be used as gage pressure transducers by connecting only one of the two ports. Pressure transducers contain a pressure sensitive diaphragm with strain gages bonded to it. The strain gage converts the deflection of the diaphragm into a measurable voltage. The strain gage output is affected by temperature changes and the zero value (no applied pressure) would normally vary from sensor to sensor. Pressure transducers contain circuitry to compensate for temperature and to correctly zero the output. Data Acquisition System Pressure transducers produce a voltage output that is proportional to the pressure applied. The output voltages are all monitored by a dedicated "data server" computer with a multi-channel data-acquisition system. The data server sends the digitized voltage data to client computers on demand across the Internet. Easy Data software logs onto the data server, receives the digitized voltage data and converts the voltage data to the measured physical property using an appropriate conversion. A linear conversion of the form Y = a( V V 0 ) 1.1 is used to convert voltage to pressure. V is the measured voltage, V 0 is a voltage offset, and the coefficient a is such that Y has the desired physical units. The Easy Data software can be used to average the voltage signal and to log the data to disk. In this lab, it will not be necessary to save the data to disk. It will be easier to simply record the pressure measurements by reading the values on the computer display.

2 Pressure Transducer Calibration The pressure transducer used for this experiment measures the differential pressure between two ports. The pressure transducer has a range of 0 to 6.8 kpa with a corresponding output voltage range of 0 to 16.7 mv. The pressure transducer can be calibrated to determine the actual relationship between volts (the measured signal) and pressure differential by connecting a pressure transducer to a static column of water. Alternately, the relationship between pressure and voltage can be obtained from the pressure transducer specifications ( A conversion based on the pressure transducer specifications will be used in this exercise. Error Analysis Both the pressure transducers and the data acquisition system contribute to the measurement errors. The pressure transducers have an accuracy of 1% FS (FS is their full-scale measurement) and a hysteresis and repeatability of 0.2% FS. The data acquisition system is set to measure a range of ±20 mv. The data acquisition system is 12-bit meaning that the measured voltage range is digitized into 2 12 (4096) intervals. The smallest difference that the data acquisition system can measure is 40 mv/4096 or 10 µv. In this case the digitization error is much smaller than the pressure transducer error. Statics Pressure variation with depth in a constant density fluid is linear. p = γ h 1.2 The simple relationship between pressure and depth suggests that pressure transducers can be used to measure pressure or depth by simply applying an appropriate calibration constant. With appropriate conversions it is also possible to measure the volume of water in a tank. Bubbler system Bubbler systems are used by United States Geological Survey (USGS) to measure stage (depth) of streams and rivers. Stations that use a bubbler system can be located hundreds of feet from the stream. In a bubbler system, an orifice is attached securely below the water surface and connected to the instrumentation by a length of tubing. Pressurized gas (usually nitrogen or air) is forced through the tubing and out the orifice. Because the pressure in the tubing is a function of the depth of water over the orifice, a change in the stage of the river produces a corresponding change in pressure in the tubing. Changes in the pressure in the tubing are recorded and are converted to a record of the river stage (depth). The accuracy of bubbler system is affected by the head loss of the gas flowing through the tubing that connects the pressure transducer to the river. If the gas flow rate is variable, the head loss through the tubing will also be variable. If the head loss in the tubing is small relative to the desired accuracy of water depth measurement then small changes in flow rate will be insignificant. A final source of error is the pressure variation due to the formation of small air bubbles at the end of the tube. The small radius of curvature of the bubbles can result in a significant pressure increase in the gas line. As the bubbles are formed the radius of curvature will vary from close to infinite to the radius of the released bubbles and the pressure in the line will vary. p = 2σ r 1.3

3 Experimental Methods Connect and Calibrate Pressure Transducer Verify that a 7-kPa pressure transducer is connected to one of the numbered ports on the middle row on the bench top. Start the Easy Data software (available in the runtimes folder on the desktop). Test the pressure sensor by pushing a finger against one of the ports and watching to see if the pressure reported by the Easy Data software changes. Peristaltic Pump (3) kpa Pressure Sensor (6) 5 7 SS Tubing (9) 2 Figure 1-2. Schematic of the bubbler system. See Table 1-1 for key to locations Click on to get a line plot of pressure vs. time. Note that you can freeze the data by clicking on. The software continues to acquire data, but the blue areas of the display are locked. For this lab you will need the Power User features. Press F1 on your keyboard to get more functions. Table 1-1. Guide to location of parts used to build the bubbler. reference item location 1 #16 Pharmed Tubing Isle End Island 4 Drawer 8 2 1/4" barbed fitting Isle End Island 4 Drawer 1 3 Peristaltic pump Oven Bench Door 3 4 1/4" quick connect T Isle End Island 4 Drawer 1 5 Short piece of #16 Pharmed Back of Peninsula 4 Drawer 1 6 Pressure Sensors South wall next to Fume Hoods 7 1/4" flexible hard tubing Isle End Peninsula 4 Right 8 1/4" quick connect elbow Isle End Island 4 Drawer 1 9 1/4"x70 cm SS tubing Oven Bench Drawer cm diameter tank Back of Peninsula 3 hanging cabinet Ruler Drawer 2 at your station Build and Test a Bubbler System Use the plumbing supplies on your bench top to build a bubbler system (Figure 1-2) and Table 1-1. You will be using the bubbler system to measure the pressure as a function of depth in a 10- cm diameter column of water. Use the peristaltic pump as your air supply. The 6 mm diameter stainless steel tube can be submerged to variable depths in a tank of water to test your bubbler system. Make sure the pump is pumping in the correct direction and that the pressure sensor is installed with the high pressure port (Figure 1-3) attached to the tubing. The low-pressure port is connected to the atmosphere so that the sensor measures gage pressure (the difference between atmospheric pressure and the pressure at a point in the system). Have the TA check your bubbler system after you've built it. The plumbing connections are made by firmly pushing the tubing (or the smooth end of the barbed fittings) into the High pressure port Low pressure port quick connectors while slowly twisting the tubing. The Figure 1-3. Pressure sensor ports.

4 connections will leak if they are not fully engaged! To disassemble a quick connector it is necessary to depress the gray collar toward the quick connect fitting while pulling the tube out of the quick connector. 1) Set the peristaltic pump rate so that a bubble is formed every 1 to 5 seconds. 2) Calibrate the bubbler by resting the bottom elbow on the bottom of the tank and then adding 500 ml of water to the tank. Measure the depth of water using the ruler. Use the control to the right of the graph to set the desired sensor output. Enter the measured depth in the target value and the press to change the sensor output to the desired value. 3) Record the depth of submergence measured using the ruler and that obtained using the bubbler system at 5 different depths (repeatable depth increments can be created by measuring out 500 ml volumes of water). 4) Use the bubbler system to determine if pressure is a function of the diameter of the reservoir. Explain your test method and your results. 5) Use the bubbler system to determine if the pressure at a point is a function of direction. Explain briefly how you tested your hypothesis and report the results obtained. 6) What happens if you don t pump air through the bubbler? Pull the bubbler out of the water and then submerge it and note what happens to the pressure reading. 7) Explain why it is necessary to continually pump air through the bubbler. 8) Observe the response of the bubbler system to rapid changes in submergence. Rapidly plunge the bubbler tube to the bottom of the reservoir and observe the response of the pressure transducer using the Signal Monitor Table 1-2. Recommended measurements. Added Volume (ml) Depth Using Ruler (cm) software. What happens to the rate of bubble formation? 9) Explain why the bubbler system responds slowly to changes in depth. Bubbler Depth (cm) Difference between Ruler & Bubbler (cm) 10) What two things could you do to decrease the response time? Try one of these and report what you find. 11) What equations would you use to determine the location of the air-water interface inside the bubbler tube if you weren t pumping air and you submerged the bubbler tube to the bottom of the tank? 12) Open the pump head on the peristaltic pump so you can see the working parts and then explain how the pump works. Measure the Elevation of a Reservoir Surface The distilled water system is fed by a reservoir located somewhere in Hollister Hall. The TA has setup a station where you can use a 200-kPa pressure transducer to determine on which floor the reservoir is located. Note that distilled water taps have white handles.

5 1) Determine the elevation difference between the lab bench tops and the water surface of the distilled water reservoir. Measure the pressure at the bottom of a tank of water in free fall The TA will demonstrate the pressure dependency on acceleration by placing a tank of water in free fall while the pressure sensor at the bottom of the tank is monitored at 100 Hz. Use the freeze function and then the zoom function to zoom in on the time when the tank was in free fall. 1) Explain how you think the pressure varied in the fluid when it was in free fall. 2) What happened to the pressure when the TA caught the tank and stopped the free fall? Lab Report Write your answers in a word document and the document to the TA at the end of lab.

6 Lab Prep Notes Table 1-3. Equipment list. Description Supplier Catalog number #/group Pressure Omega PX26-001DV 1 transducer Pressure transducer Omega PX26-030DV 1 per class 4 L volumetric CEE shop 1 detector 45 cm ruler 1 Peristaltic pump Cole- 1 Parmer #16 Pharmed tubing Cole- Parmer 1 TA notes 1) Prepare a station for each team of 2-3 students. 2) Place all the necessary pieces of equipment on the workbench, but do not assemble the apparatus. 3) Plug both ports on the bottom of the 10 cm diameter cylinder so that it is ready to fill with water. 4) Plug a 7 kpa pressure sensor into the 2 nd row of ports. 5) Install the #16 Pharmed tubing in the peristaltic pump. 6) Provide each team with a 1 liter plastic beaker (to add water to the cylinder) and a 100 ml plastic graduated cylinder (to measure the effects of a different diameter). 7) Create configuration files for each workstation so that when Easy Data is launched it immediately begins acquiring data from the 7 kpa sensor on their benchtop. 8) Make sure that the voltage range on the 2 nd row of ports is 20 mv. If necessary changes this on the DataServer computer. 9) Make sure that the voltage range on the 1 st row of ports is 500 mv. 10) Setup one station (this could either be one of the student stations or an extra station) with a 200 kpa pressure sensor and a tube connecting it to the distilled water tap. Have the students use this station to measure the height of the distilled water tank. 11) Setup one station (this could either be one of the student stations or an extra station) with a 7 kpa pressure sensor connected to the bottom of one of the 10 cm diameter cylinders. Set the data acquisition rate to 100 Hz. Use this station to demonstrate the effects of free fall. At the beginning of class give a quick demonstration of the following: 1) Make a connection with a quick connector and then take it apart. 2) Change the direction and flow rate of a peristaltic pump. 3)?