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Pressure Definitions Pressure

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Pressure Definitions Pressure Dr. Christopher M. Godfrey University of North Carolina at Asheville Pressure Definitions Pressure Absolute Gauge Differential Absolute pressure Gauge pressure Differential pressure Total static pressure Pressure relative to Pressure relative to exerted by gas/fluid atmospheric pressure another pressure Barometric pressure e.g., pressure in a tire Gauge pressure is a special case of differential pressure ATMS 320 – Fall 2011 Photos: http://www.barometerworld.co.uk/ ATMS 320 – Fall 2011 Let’s make an instrument: Manometer Let’s make an instrument: Manometer To measure atmospheric pressure, we p − p p p = 0 h = 2 1 1 p2 close off one end of the manometer 1 p tube. ρfluid g p1 – ambient pressure (not p necessarily atmospheric h = h pp)ressure) h ρfluid g p2 – gauge pressure Here, we’re measuring differential pressure (two unknown pressures). In In normal operation, we straighten out meteorology, we want to measure the the tube, invert it, and place the open absolute pressure… end in a reservoir of mercury ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Mercury Barometers Mercury (Fortin) Barometers The Fortin design: Improved version of mercury barometer (level of cistern maintained at zero of scale) High accuracy Easy calibration Mercury enclosed in a glass tube that is sealed at the top Almost a vacuum Pressure = vapor pressure of Hg + residual gas Mercury reservoir at the bottom Level of mercury in reservoir is adjusted to a reference (fiducial) point ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 1 Vernier Scale Mercury Barometer Errors Gas in the vacuum space The pressure of any gas in the vacuum space will tend to counteract the pressure being exerted by the atmosphere If we tilt the barometer, a true vacuum won’t create a bubble (please don’t try this with the department’s barometer…not that you could anyway /) What can get in there? Mercury vapor – very small error (low vapor pressure) Air Water vapor – potentially large error ReadingWhat is the reading for each of these Readingvernier scales? 10 μg of water vapor can potentially cause a 2.3-mb error at normal atmospheric pressures 911.80 mb No peaking… 915.65 mb ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Mercury Barometer Errors Mercury Barometer Errors: Capillary depression of the mercury surface Index Correction This error is typically small and known Narrowing of the tube can cause changes to the mercury The index correction (Cx) is a table of meniscus corrections that account for slight imperfections of the tube diameter and vacuum that are inevitable during FdiFor a 5 mm diameter manufacture tube, the error can be h > h as large as 2.00 mb 2 1 Values are supplied to the user by the For a 13 mm diameter manufacturer tube, the error can be Assume Cx = 0 if not specified as large as 0.27 mb Values are found by calibrating the Correction for this error is incorporated into the instrument with a reference instrument index correction ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Mercury Barometer Errors: Mercury Barometer Errors: Non-uniformity of temperature Temperature Correction Changes in temperature can affect the Mercury is used in thermometers because it expands and contracts with changes in expansion and contraction of the mercury temperature column and the attached metal scale Temppgerature gradients along the mercury Meeatal column can vary that expansion or Scale CT = −p1(β −α)T contraction in an unknown manner The pressure error is a function of the difference between the change in the Most Fortin barometers are housed in a column height and linear expansion of closed environment to prevent temperature the scale due to changes in (but not pressure) fluctuations temperature. Here, T is the temperature in °C and This barometer is enclosed in a case p1 is the measured pressure. http://www.physics.indiana.edu/~meyer1/historinstr/other.html ΔV =βVΔT ΔL = αLΔT ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 2 Mercury Barometer Errors: Mercury Barometer Errors: Correctable Error Correctable Error Now we have several corrections that we can Now we have several corrections that we can apply in order to obtain the “best” pressure apply in order to obtain the “best” pressure measurement possible: measurement possible: p2 = p1 + CX + CT p2 = p1 + CX + CT p1 = Barometer reading p1 = Barometer reading CX = Index correction CX = Index correction CT = Temperature correction CT = Temperature correction But wait, there’s more… Watch this! ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 http://www.atmospheric-violence.com/ Mercury Barometer Errors: Dirt Dirty mercury Difficult to see when the fiducial point touches the mercury Hard to read the meniscus Impurities can affect density Dirty scale Hard to read the scale Corrosion could affect the expansion coefficient http://www.psych.ndsu.nodak.edu/brady/ ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Mercury Barometer Errors: Dynamic Wind Effects Barometer not mounted vertically Typically small errors We usual want to measure only the static At 1000 mb, barometer must be kept within pressure 1.5 mm of vertical in order to keep error to Dynamic pressure affects all barometers and within 0. 026 mb. is due to air motion around the barometer To avoid the influence of pressure variations inside buildings (due to ventilation systems, open windows, closing doors, etc.), these errors can be reduced using a pressure vent to the outside (a static port) ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 3 Dynamic Wind Effects 1 Δp = CρV 2 2 ρ is the air density V is the fluid speed C is the pressure coefficient Usually close to unity http://www.atomicarchive.com/Effects/effects3.shtml Positive or negative Depends on shape of barometer and wind direction ATMS 320 – Fall 2011 Aneroid Barometer Aneroid Barometer Aneroid: without fluid Calibration equation for a flat diaphragm a- (without) + nero- (water) + -oid (resembling) 4 ⎡ 3 ⎤ Evacuated chamber with a flexible diaphragm 16Et y ⎛ y ⎞ p = 4 2 ⎢ + 0.488⎜ ⎟ ⎥ Deflection of diaphragm is proportional to 3R ()1− v ⎣⎢ t ⎝ t ⎠ ⎦⎥ atmospheric pressure p = pressure (Pa) E = modulus of elasticity (N m-2) The spring keeps the y = deflection of the diaphragm center (m) diaphragm from t = diaphragm thickness (m) collapsing R = diaphragm radius (m) v = Poisson’s ratio (related to ratio of lateral to axial strain) ≈ 1/3 for metals ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Aneroid Barometer Aneroid Barometer Calibration equation for a flat diaphragm Static sensitivity for a flat diaphragm Define the deflection ratio as the ratio of the The static sensitivity is the derivative of the diaphragm deflection to the diaphragm thickness: y deflection ratio (yr) with respect to pressure y = r t (p): dy 1 Substitute into calibration equation for flat r = 2 diaphragm aneroid cell: dp c o + 3c 0 c1 y r p = c y + c y3 0 [ r 1 r ] Static sensitivity decreases as pressure increases and the diaphragm is forced to Note that c0 and c1 are not the coefficients for a linear fit, but are instead the constant values from the greater deflections calibration equation ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 4 Aneroid Barometer Aneroid Barometer Static sensitivity Transfer equation for a corrugated diaphragm 5 2 −1.52 Adding corrugations vastly improves linearity y 2.25×10 D(1− v ) ⎛ t ⎞ yr = = ⎜1000 ⎟ p and increases static sensitivity at higher t tE ⎝ D ⎠ pressures p = pressure (Pa) E = modulus of elasticity (N m-2) y = deflection of the diaphragm center (m) Flat t = diaphragm thickness (m) R = diaphragm radius (m) v = Poisson’s ratio (related to ratio of lateral Corrugated Corrugated to axial strain) ≈ 1/3 for metals Diaphragm D = 2R yr ~ (constant) p ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Aneroid Barometer Aneroid Barometer Mechanical Output Electrical Output Deflection of a single Piezoresistor aneroid is typically small; Resistance changes in response to an applied force that multiple chambers amplify deforms the resistor the deflection Capacitive transducer As diaphragm deflects, the distance between capacitor plates changes , changing the capacitance ε A C = 0 d C = capacitance ε0 = permittivity of free space A = area of plate Aneroid capsule with a capacitive transducer d = distance between plates Aneroid Barograph ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Aneroid Barometer Aneroid Barometer Electrical Output Vaisala PTB101B Pressure Transmitter Most barometers in use Uses a silicon capacitive pressure transducer today are aneroid 5 mm Silicon diaphragm Very small Low leakagg(e (excellent vacuum) Linear deflection Can compensate for temperature-induced errors (mostly) Photo: C. Godfrey ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 5 Aneroid Barometer Direct vs. Indirect Pressure Sensors Vaisala PTB101B Pressure Transmitter So far, we’ve learned about Microprocessor functions direct pressure measurements… Control Controls all aspects of the sensor such as when to take a measurement and when to send out results Communications Calibration Computes the calibration function in real time; data transmitted to user are already calibrated What about indirect ways to Diagnostics Modern equipment can detect a malfunctioning sensor measure pressure? Indirect techniques do not respond directly to pressure, but instead respond to some other variable http://whatscookingamerica.net/boilpoint.htm that is a function of pressure ATMS 320 – Fall 2011 ATMS 320 – Fall 2011 Hypsometer Hypsometer One indirect method uses a fundamental physical Since a boiling fluid has a vapor standard:
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