Lab 1: Pressure and surface tension. Bubblers, gravity and the mighty paper clip.

Transcription

1 Lab 1: Pressure and surface tension. Bubblers, gravity and the mighty paper clip. CEE Summer 2012 SAFETY The major safety hazard in this laboratory is a shock hazard. Given that you will be working with water and items running on standard line voltages (the pump and the computer) you should pay attention to the possibility of electric shock. If water spills on the desktop, please clean it up IF there is no risk of shock. If water gets near a 110V electrical connection (i.e. a wall outlet or anything connected to it) DO NOT clean it up. Seek a TA, Tinoco (HLS 369), or one of the CEE technicians (Tim Brock, Paul Charles, or Cameron Willkens, who have offices across from the lab) for help. Always work with a minimum of two people. OBJECTIVES In this laboratory you will: 1. Measure pressure using a computerized data acquisition system. 2. 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. The bubbler system is a model of typical systems used by the United States Geological Survey (USGS) to monitor river stage (depth). 3. Experiment with pressure on an object (the bubbler) in freefall, and 4. Look with a critical eye at surface tension. THEORY Pressure Transducers A transducer is any device that converts energy of one form, in this case pressure work done on an elastic membrane, to energy of another form, in this case an electrical voltage. Pressure transducers produce a voltage output that is proportional to the applied pressure. Pressure transducers are available in gage, 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. Our pressure transducers contain a flexible diaphragm with strain gages bonded to it. The strain gage converts deflection in the diaphragm due to the applied pressure difference into a 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 zero the output (i.e., for a gage transducer to read zero under atmospheric pressure). Our sensors are cheap so they need to be re-zeroed regularly and we provide a software method for doing this. Data Acquisition System Pressure transducers produce a voltage output that is proportional to the applied pressure difference. The output voltages are all sampled by a data acquisition card which is controlled by a dedicated data server computer. Software receives the digitized voltage 1

2 data and converts it to the measured physical property using a conversion of the form: Y = a(v V 0 ) b (1) where V is the measured voltage, V 0 is a voltage offset, the coefficients a and b are user defined, and Y has the desired physical units. The voltage offset is how the sensor is zeroed and it may be measured at a reference pressure such as atmospheric pressure. We will use Easy Data software, which can monitor any voltage data being acquired using the data server. It is capable of monitoring eight channels per lab station at once. Additionally, each channel can be calibrated for its own unique data monitoring hardware. To launch Easy Data, double-click on the Easy Data icon on the desktop, generally the lower left of all the icons. Pressure Transducer Calibration The pressure transducer used for this experiment (shown in Figure 1 ) measures the differential pressure between two ports. The pressure transducers for this lab have a range of 0 to 6.8kPa. 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 ( For this semester we have permanently selected the factory provided calibration of the sensor so the output is units of Pascals (Pa). Accuracy Both the pressure transducers and the data acquisition system contribute to the measurement errors. According to the manufacturers specifications the pressure transducers we are working with have an accuracy of 1% FS (FS is their full-scale measurement) and a hysteresis and repeatability of 0.2% FS. Figure 1: Differential pressure transducer with tubes connected to each port. Statics Pressure variation with depth in an incompressible fluid is linear: p = γh (2) The simple relationship between pressure and depth suggests that pressure transducers can be used to measure either pressure or depth. Bubbler System Bubbler systems are used by the 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. The accuracy of a bubbler system is affected by pressure losses due to frictional effects of the gas flowing through the tubing (we will see this later in the semester, both in class and lab!). Another source of error is the pressure variation due to the formation of small air bubbles at the end of the tube. The 2

3 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. We should expect this as for spherical bubbles we know the pressure is inversely related to the radius: p = 2σ r (3) Freefall Experiment The second part of this lab is a brief experiment that explores the nature of pressure in a fluid in freefall. You will simply be measuring the water pressure inside the bubblers prior to, during, and after a drop. Would you feel the water pressure around you if you were to swim over Niagara Falls? You will find out by doing this experiment! Surface Tension and Free-Body Diagrams The final part of this lab is to do some critical viewing of surface tension in action and sketch the appropriate free-body diagram. DATA ACQUISITION Software Start the Easy Data software bring up the software control palette (shown in Figure 2). The software displays pressure values in Pascals from a pressure transducer that has been connected to one of the numbered ports on the Data Acquisition Interface Box (DAIB) (see Figure 3). The ports on the DAIB are numbered and the numbers correspond to channels in the Easy Data software. The software should be configured to immediately begin this lab. The pressure sensor should be in the AI0 port (upper-left). Drag the mouse over the buttons on the program for hints on what tasks they perform. You will notice that as soon as you open the software, it begins to read the pressure values being measured by the transducer (assuming the transducer is plugged into the DAIB). Note that these values are not being Figure 2: Easy Data Acquisition screen recorded, but are only flashing on the screen in real time (the red flashing button on the upper right indicates data not being saved ). Throughout this lab, you will have the option to log your pressure data to a file for future use by clicking the log button. The first time you do this, you need to make a directory for your group in the folder on the desktop titled CEE3310. The full path if you need it will be: C:\Documents and Settings\Lab\Desktop\CEE3310\YourTeam sname\ For the entire semester you can keep your data files collected in labs here. If you want to move a file from the computer someplace else these computers are on the network. The computers have a USB slot in front so you can take files with you using a USB memory stick as well. Note that the software is currently set up to sample at a maximum frequency of 500 Hz (you will use this frequency for the freefall portion of the lab). Often times, however, it is more convenient to record your data at a lower frequency. If you choose a slower frequency, the Easy Data software internally records data at the higher rate, but will only report the average value over the time period you have chosen (i.e., if you choose 1 Hz, it will take the average of all 500 measurements it took over every second and report it as one value). Prior to starting the lab, it is highly recommended that your group takes about two minutes to practice using the software and get comfortable with each of 3

4 plastic tube is used to measure the relationship between depth and pressure. Figure 3: Data Acquisition Interface Box the main features (i.e., zeroing, freezing the screen, toggling between plot types, locking/unlocking plot view, and adjusting the sample frequency). Knowing how to use the software will significantly cut the time you spend in the lab! EXPERIMENTAL PROCEDURES If you have signed up for a TA-available slot the TA will meet you at the beginning of lab (please be on time), but then they will go and do their own work. The TA s will let you know where they will be/how to contact them at the beginning of lab so you can find them when you re ready for checkout. If you sign up when they are not available, schedule a meeting with them or Tinoco to check out. A) Experimental Procedure - Bubbler A 10cm diameter tube that can be filled with up to 50cm of water is used to model a small reservoir (see Figure 4). A pressure transducer connected to a clear Figure 4: Experimental apparatus The pressure transducer is connected to a port in the DAIB. Use the peristaltic pump (shown in Figure 4) as your air supply. The 6mm diameter tube can be submerged to variable depths in the tank of water to test your bubbler system. The pump begins pumping air when start is pressed. Adjust the flow rate by using the up and down arrows to the right of the displayed numbers so that a bubble is formed every 2 to 5 seconds. Note that the motor direction is always clockwise for this pump, and because you want to push air out of the bubbler, you should attach the tube to the right side of the pump (if you attach the tube to the left side you will suck water out of the cylinder and pump it all over the desk). Ensure that the 7kPa pressure transducer is plugged into the correct channel on the DAIB. Verify that the Easy Data software is set-up for the 7kPa sensor (see right side of main screen). 1. Prior to logging any data, you need to be sure to zero the pressure sensor (you are accounting for drift and atmospheric pressure changes and telling Easy Data that you want the current pres- 4

5 sure in the room to be considered 0, or atmospheric pressure in gage). Do this by removing the entire bubbler tube from the water and then zero the sensor with the Easy Data software. Obtain the following data sets (Be sure you re logging your data!): 2. Submerge the bubbler rod to a selected depth (with the air pump running). Record pressure data with Easy Data software for a minimum of 1 minute (see instructions above) at the sample frequency of 5 Hz. Repeat this step for a total of 5 different depth measurements. To ensure repeatability, measure the pressure at each of the five depths again (for a total of two one-minute measurements at each depth). 3. Choose any depth for this measurement. Start with the bubbler pumping air, and then, using the stop button on the pump, stop the flow of air. Perform this measurement twice at the same depth. Log the data for two-minutes after you stop the bubbler. 4. Submerge the bubbler to a shallow depth with the bubbler pumping air. Once the pressure stabilizes, rapidly submerge the bubbler to a much deeper depth. Allow time for the pressure to stabilize once again. Then, rapidly return the bubbler to a roughly similar shallow depth (it does not have to be the same exact shallow depth). Log data until the pressure stabilizes once again. Repeat this experiment twice. Checkout A1. Using Excel or Matlab, open the data you collected for part one, and plot the relationship between pressure and depth. Does the relationship between the two measurements seem to match the result predicted in Eq. 2? Calculate the specific weight of water, γ, from this data. Does the value of γ match the value tabulated in the book? Discuss. A2. Discuss what you saw when you turned off the pump. Could you see the bubble? Does the pressure measurement in your data agree with what you saw at the moment of air-flow stoppage? Explain how the formation of bubbles at the end of the tube can cause error in this method of measurement (Hint: It may help to closely observe 10 seconds of your data that was collected during bubbling... do you see a pattern?). A3. Explain why it is necessary to continually pump air through the bubbler. A4. What happened to the rate of bubble formation during the rapid changes of depth? Explain why the bubbler system responds slowly to some changes in depth (include example plots from your data). What could you do to decrease the response time? B) Experimental Procedure - Freefall 1. Increase sample frequency to 500Hz and ensure that data is registering on the screen 2. Clamp bubbler tube (lightly just enough to hold it don t crush it!) to the side of the cylindrical tank. 3. Begin logging data. 4. Raise entire bubbler system off desk to eye level holding with BOTH hands low on the cylinder. 5. Pull hands simultaneously JUST away from cylinder sides and CATCH the cylinder before the top passes below your hands! For this to work you must have a moment when BOTH hands are OFF the cylinder and it is free falling. It may be convenient to have somebody man the computer screen during the drop and click the Freeze button shortly after the bubbler drops to examine the pressure changes while they are still on the screen. 6. Perform the bubbler drop experiment three separate times (steps 3-5). 5

6 When you have completed the lab, prepare your answers to the "Checkout" questions and find one of the TA s. Please have everything in presentable form. This means label Excel/Matlab plots and have them up on the computer screen, have all sketches completed, and be ready to answer all of the "Checkout" questions to the best of your ability. You don t need to have written answers. Figure 5: Bending the paper clip (left). Pushing the paper clip through the water surface and pulling it back out again (right). Checkout: B1. What happened during the freefall? What are your thoughts on this? C) Experimental Procedure Surface Tension This short part of the lab has nothing to do with the bubbler system. You will use a paper clip to explore surface tension a little more. You will find a small plastic cup and some paper clips on the lab table. Fill the cup with water. Take one of the paper clips and bend it as illustrated in Figure 5. Now, carefully watch the water surface as you push the paper clip through the surface and pull it back out again as shown in Figure 5. Notice which way the water surface bends. Try to float an un-bent paper clip on the surface of the water (Hint: make sure the paper clip is dry). Checkout: C1. Sketch a free-body diagram of the paper clip as you push it down through the water surface (at the instant before the surface breaks). Also sketch the water surface, showing the way it bends near the paper clip (note that the water surface is not part of the free body diagram of the paper clip, but you can sketch it in the same picture if you like). C2. Sketch a free-body diagram of the paper clip as you pull it up through the water surface. Also sketch the water surface near the paper clip. 6