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 alon g the mercur y 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: The boiling point pressure that is equal to the of a liquid atmospheric pressure, we can use „ The boiling point of a liquid the Clausius-Clapeyron equation: depends on temperature ⎡ L ⎛ 1 1 ⎞⎤ andIfd pressure: If we p = p0 exp⎢ ⎜ − ⎟⎥ R ⎜ T T ⎟ measure the temperature, ⎣ ⎝ 0 ⎠⎦ we can solve for the p0 = sea-level pressure (101,325 Pa) pressure T0 = boiling point at sea-level pressure (373.15 K for H2O) „ The instrument that does 6 -1 L = latent heat of vaporization (2.5E J kg for H2O) this is called a hypsometer -1 -1 R = gas constant (461.5 J kg K for H2O vapor) T = temperature of vapor

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

Hypsometer Advantages of a Hypsometer

„ Recall that the static sensitivity is the slope of the transfer function „ No aneroid chamber „ Consider the transfer function for two „ No mercury hypsometric fluids „ Can be small „ CbCan be au toma tdted Poor static sensitivity at high pressures „ Portable (used on old radiosondes) „ No corrections needed for gravity or temperature „ No drift or hysteresis

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

6 Disadvantages of a Hypsometer Current Barometric Measurements „ Extremely non-linear ASOS: Setra Model 470 „ Need to routinely replace the hypsometric Range: 600–1100 mb Inaccuracy: ±0.02% full scale fluid Resolution: 0.01 mb „ Need substantial power to boil the fluid „ Not as small as modern aneroid barometers „ Need accurate temperature sensor and associated electronics „ Need excellent coupling of the vapor and the Oklahoma Mesonet: temperature sensor Vaisala PTB220

Range: 500–1100 mb Inaccuracy: ±0.25 mb Resolution: 0.1 mb Inside the Vaisala PTB220

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

Current Barometric Measurements Exposure Error Vaisala RS80 Radiosonde „ One of the largest pressure errors is Range: 3–1060 mb Inaccuracy: ±0.5 mb attributed to dynamic wind effects Resolution: 0.1 mb „ Consider this… Used in twice daily NWS soundings You are driving a mobile mesonet vehicle at 25 m s-1 into a rear flank downdraft that has a surface wind speed of 30 m s-1 (directly toward the vehicle). What is the dynamic wind error in the pressure measurement? (Let C=1) CρV 2 Δp = 2 2 This is a 1.0(1.25 kg m-3 )(55 m s-1 ) Δp = huge error! 2 Vaisala’s latest radiosonde: RS92 Δp =18.9 mb

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

Static Pressure Port Static Pressure Port We need a device that will remove the dynamic This is nice, but the flat plate has a problem when wind effects and will allow a measurement of the wind is incident upon the port at an angle static pressure without error

Wind blowing at an angle to the plate produces a non-zero pressure coefficient (C) and hence the plate does not eliminate dynamic wind effects Wind Wind

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

7 Dual-Plate Static Pressure Port Quad-Plate Static Pressure Port

To improve upon this Another design further reduces angle errors direction problem, engineers devised a dual-plate port „ Used in VORTEX „ Mounted upside down „ Even better error results

„ Used in buoys „ Mounted vertically „ Better error results

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

Barometer Comparison Barometer Comparison

„ Mercury (Fortin) Characteristics „ Aneroid Characteristics ‰ Easy to calibrate, but you need an accurate scale and a ‰ Non-linear good temperature sensor ‰ Temperature sensitive, usually in a complex way ‰ Simple theoretical model ‰ Subject to unpredictable drift (needs frequent ‰ Must be vertical during operation recalibration) ‰ Difficult to transport ‰ No gravity correction required ‰ Requires temperature and gravity correction ‰ Very small ‰ Vacuum and/or mercury contamination causes errors ‰ Low power consumption ‰ Mercury vapor is toxic ‰ Insensitive to orientation, motion, and shock; very ‰ Height of column cannot be reduced portable ‰ Hysteresis effects due to mercury sticking to glass ‰ Easily automated ‰ Very difficult to automate

ATMS 320 – Fall 2011 ATMS 320 – Fall 2011

Barometer Comparison

„ Hypsometer characteristics

‰ Extreme non-linearity

‰ Best sensitivity at low pressure

‰ Easy to calibrate

‰ Requires very accurate temperature sensor

‰ Sensitive to orientation, but reasonably portable

‰ No gravity or temperature correction

‰ Easily automated

ATMS 320 – Fall 2011

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