Statics: Pressure MeasurementObjectivesTheoryPressure TransducersData Acquisition SystemPressure Transducer CalibrationError AnalysisStaticsBubbler systemExperimental MethodsConnect and Calibrate Pressure TransducerBuild and Test a Bubbler SystemTable . Guide to location of parts used to build the bubbleTable . Recommended measurements.Measure the Elevation of a Reservoir SurfaceMeasure the pressure at the bottom of a tank of water in freLab ReportLab Prep NotesTable . Equipment list.TA notesStatics: 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, 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 ()0YaVV=− 1.1 is used to convert voltage to pressure. V is the measured voltage, V0 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. Figure 1-1. Differential pressure transducer.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 (http://www.omega.com/Pressure/pdf/PX26.pdf). 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 212 (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. phγ= 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. 2prσ= 1.3Experimental Methods Connect and Calibrate Pressure Transducer Verify that a 7-kPa pressure transducer is connected to one