Let’s make an instrument: Manometer - UNC A pressure Pressure relative ... Absolute Gauge...

1

PressureDr. Christopher M. GodfreyUniversity of North Carolina at Asheville

Photos: http://www.barometerworld.co.uk/ATMS 320 – Fall 2011

Pressure Definitions

ATMS 320 – Fall 2011

Absolute pressureTotal static pressure exerted by gas/fluidBarometric pressure

Gauge pressurePressure relative to atmospheric pressuree.g., pressure in a tire

Differential pressurePressure relative to another pressureGauge pressure is a special case of differential pressure

Absolute Gauge Differential

Let’s make an instrument: Manometer

p1 – ambient pressure (not necessarily atmospheric pressure) h

p1 p2

gpph

fluid

12

ρ−

=


p )p2 – gauge pressure

Here, we’re measuring differential pressure (two unknown pressures). In meteorology, we want to measure the absolute pressure…

To measure atmospheric pressure, we close off one end of the manometer tube.

h

Let’s make an instrument: Manometerp1 = 0 p

gph

fluidρ=


gfluidρ

In normal operation, we straighten out the tube, invert it, and place the open end in a reservoir of mercury

Mercury Barometers


The Fortin design:Improved version of mercury barometer (level of cistern maintained at zero of scale)

High accuracyEasy calibration

Mercury enclosed in a glass tube

Mercury (Fortin) Barometers


Mercury enclosed in a glass tube that is sealed at the top

Almost a vacuumPressure = vapor pressure of Hg + residual gas

Mercury reservoir at the bottomLevel of mercury in reservoir is adjusted to a reference (fiducial) point

2

Vernier Scale


Reading911.80 mb

Reading915.65 mbNo peaking…

What is the reading for each of these vernier scales?

Mercury Barometer ErrorsGas in the vacuum space

The pressure of any gas in the vacuum space will tend to counteract the pressure being exerted by the atmosphereIf we tilt the barometer, a true vacuum won’t create a bubble (please don’t try this with the


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)AirWater vapor – potentially large error

10 μg of water vapor can potentially cause a 2.3-mb error at normal atmospheric pressures

Mercury Barometer ErrorsCapillary depression of the mercury surface

This error is typically small and knownNarrowing of the tube can cause changes to the mercury meniscus

F di


12 hh >For a 5 mm diameter tube, the error can be as large as 2.00 mbFor a 13 mm diameter tube, the error can be as large as 0.27 mbCorrection for this error is incorporated into the index correction

Mercury Barometer Errors:Index Correction

The index correction (Cx) is a table of corrections that account for slight imperfections of the tube diameter and vacuum that are inevitable during


manufactureValues are supplied to the user by the manufacturer

Assume Cx = 0 if not specifiedValues are found by calibrating the instrument with a reference instrument

Mercury Barometer Errors:Non-uniformity of temperature

Mercury is used in thermometers because it expands and contracts with changes in temperatureTemperature gradients along the mercury


p g g ycolumn can vary that expansion or contraction in an unknown mannerMost Fortin barometers are housed in a closed environment to prevent temperature (but not pressure) fluctuations

http://www.physics.indiana.edu/~meyer1/historinstr/other.html

This barometer is enclosed in a case

Mercury Barometer Errors:Temperature Correction

Changes in temperature can affect the expansion and contraction of the mercury column and the attached metal scale

( )TpC αβMetal


( )TpCT αβ −−= 1

TVV Δ=Δ β TLL Δ=Δ α

e aScale

The pressure error is a function of the difference between the change in the column height and linear expansion of the scale due to changes in temperature.

Here, T is the temperature in °C and p1 is the measured pressure.

3

Mercury Barometer Errors:Correctable Error

Now we have several corrections that we can apply in order to obtain the “best” pressure measurement possible:

CC ++


TX CCpp ++= 12

p1 = Barometer readingCX = Index correctionCT = Temperature correction

Mercury Barometer Errors:Correctable Error

Now we have several corrections that we can apply in order to obtain the “best” pressure measurement possible:

CC ++


TX CCpp ++= 12

p1 = Barometer readingCX = Index correctionCT = Temperature correction

But wait, there’s more… Watch this!http://www.atmospheric-violence.com/


Mercury Barometer Errors:Dirt

Dirty mercuryDifficult to see when the fiducial point touches the mercuryHard to read the meniscus


Hard to read the meniscusImpurities can affect density

Dirty scaleHard to read the scaleCorrosion could affect the expansion coefficient http://www.psych.ndsu.nodak.edu/brady/

Mercury Barometer Errors:Barometer not mounted vertically

Typically small errorsAt 1000 mb, barometer must be kept within 1.5 mm of vertical in order to keep error to within 0 026 mb


within 0.026 mb.

Dynamic Wind Effects

We usual want to measure only the static pressureDynamic pressure affects all barometers and is due to air motion around the barometer


is due to air motion around the barometerTo 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)

4

Dynamic Wind Effects

2

21 VCp ρ=Δ


ρ is the air densityV is the fluid speedC is the pressure coefficient

Usually close to unityPositive or negativeDepends on shape of barometer and wind direction

http://www.atomicarchive.com/Effects/effects3.shtml

Aneroid BarometerAneroid: without fluida- (without) + nero- (water) + -oid (resembling)Evacuated chamber with a flexible diaphragmDeflection of diaphragm is proportional to atmospheric pressure


The spring keeps the diaphragm from

collapsing

Aneroid BarometerCalibration equation for a flat diaphragm

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+

−=

3

24

4

488.013

16ty

ty

vREtp


p = pressure (Pa)

E = modulus of elasticity (N m-2)

y = deflection of the diaphragm center (m)

t = diaphragm thickness (m)

R = diaphragm radius (m)

v = Poisson’s ratio (related to ratio of lateral to axial strain) ≈ 1/3 for metals

Aneroid BarometerCalibration equation for a flat diaphragm

Define the deflection ratio as the ratio of the diaphragm deflection to the diaphragm thickness:

Substitute into calibration equation for flattyy r =


Substitute into calibration equation for flat diaphragm aneroid cell:

Note that c0 and c1 are not the coefficients for a linear fit, but are instead the constant values from the calibration equation

[ ]310 rr ycycp +=

Aneroid BarometerStatic sensitivity for a flat diaphragm

The static sensitivity is the derivative of the deflection ratio (yr) with respect to pressure (p):

1rdy


Static sensitivity decreases as pressure increases and the diaphragm is forced to greater deflections

2103 ro

r

ycccdpy

+=

5

Aneroid BarometerStatic sensitivity

Adding corrugations vastly improves linearity and increases static sensitivity at higher pressures


Flat

Corrugated CorrugatedDiaphragm

Aneroid BarometerTransfer equation for a corrugated diaphragm

pDt

tEvD

tyyr

52.125

1000)1(1025.2 −

⎟⎠⎞

⎜⎝⎛−×

==

p = pressure (Pa)

E = modulus of elasticity (N m-2)


y = deflection of the diaphragm center (m)

t = diaphragm thickness (m)

R = diaphragm radius (m)

v = Poisson’s ratio (related to ratio of lateral to axial strain) ≈ 1/3 for metals

D = 2Rpyr constant)(~

Aneroid BarometerMechanical OutputDeflection of a single aneroid is typically small; multiple chambers amplify the deflection


Aneroid Barograph

Aneroid BarometerElectrical Output

PiezoresistorResistance changes in response to an applied force that deforms the resistor

Capacitive transducerAs diaphragm deflects, the distance between capacitor plates changes changing the capacitance


plates changes, changing the capacitance

C = capacitanceε0 = permittivity of free spaceA = area of plated = distance between plates

dAC 0ε=

Aneroid capsule with a capacitive transducer

Aneroid BarometerElectrical Output

Most barometers in use today are aneroid

Silicon diaphragmVery smallLow leakage (excellent

5 mm


g (vacuum)Linear deflectionCan compensate for temperature-induced errors (mostly)

Aneroid BarometerVaisala PTB101B Pressure TransmitterUses a silicon capacitive pressure transducer


Photo: C. Godfrey

6

Aneroid BarometerVaisala PTB101B Pressure Transmitter

Microprocessor functionsControl

Controls all aspects of the sensor such as when to take a measurement and when to send out results


CommunicationsCalibration

Computes the calibration function in real time; data transmitted to user are already calibrated

DiagnosticsModern equipment can detect a malfunctioning sensor

Direct vs. Indirect Pressure SensorsSo far, we’ve learned about direct pressure measurements…

ATMS 320 – Fall 2011http://whatscookingamerica.net/boilpoint.htm

What about indirect ways to measure pressure?Indirect techniques do not respond directly to pressure, but instead respond to some other variable that is a function of pressure

HypsometerOne indirect method uses a fundamental physical standard: The boiling point of a liquidThe boiling point of a liquid depends on temperature

d If


and pressure: If we measure the temperature, we can solve for the pressureThe instrument that does this is called a hypsometer

HypsometerSince a boiling fluid has a vapor pressure that is equal to the atmospheric pressure, we can use the Clausius-Clapeyron equation:

⎤⎡⎟⎞

⎜⎛L 11


⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

TTRLpp 11exp

00

p0 = sea-level pressure (101,325 Pa)

T0 = boiling point at sea-level pressure (373.15 K for H2O)

L = latent heat of vaporization (2.5E6 J kg-1 for H2O)

R = gas constant (461.5 J kg-1 K-1 for H2O vapor)

T = temperature of vapor

HypsometerRecall that the static sensitivity is the slope of the transfer functionConsider the transfer function for two hypsometric fluids


Poor static sensitivity at high pressures

Advantages of a Hypsometer

No aneroid chamberNo mercuryCan be smallC b t t d


Can be automatedPortable (used on old radiosondes)No corrections needed for gravity or temperatureNo drift or hysteresis

7

Disadvantages of a HypsometerExtremely non-linearNeed to routinely replace the hypsometric fluidNeed substantial power to boil the fluidNot as small as modern aneroid barometers


Need accurate temperature sensor and associated electronicsNeed excellent coupling of the vapor and the temperature sensor

Current Barometric MeasurementsASOS: Setra Model 470Range: 600–1100 mb

Inaccuracy: ±0.02% full scale

Resolution: 0.01 mb


Oklahoma Mesonet: Vaisala PTB220

Inside the Vaisala PTB220

Range: 500–1100 mb

Inaccuracy: ±0.25 mb

Resolution: 0.1 mb

Current Barometric MeasurementsVaisala RS80 RadiosondeRange: 3–1060 mb

Inaccuracy: ±0.5 mb

Resolution: 0.1 mb

Used in twice daily NWS soundings


Vaisala’s latest radiosonde: RS92

Exposure Error

One of the largest pressure errors is attributed to dynamic wind effectsConsider this…

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


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)

2

2VCp ρ=Δ

( )( )2

s m 55m kg 25.10.1 21-3-

=Δp

mb 9.18=Δp

This is a huge error!

Static Pressure PortWe need a device that will remove the dynamic wind effects and will allow a measurement of static pressure without error


Wind

Static Pressure PortThis is nice, but the flat plate has a problem when the wind is incident upon the port at an angle


Wind

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

8

Dual-Plate Static Pressure PortTo improve upon this direction problem, engineers devised a dual-plate port


Used in buoysMounted verticallyBetter error results

Quad-Plate Static Pressure PortAnother design further reduces angle errors

Used in VORTEXMounted upside downEven better error results


Barometer ComparisonMercury (Fortin) Characteristics

Easy to calibrate, but you need an accurate scale and a good temperature sensorSimple theoretical modelMust be vertical during operationDifficult to transport


Difficult to transportRequires temperature and gravity correctionVacuum and/or mercury contamination causes errorsMercury vapor is toxicHeight of column cannot be reducedHysteresis effects due to mercury sticking to glassVery difficult to automate

Barometer ComparisonAneroid Characteristics

Non-linearTemperature sensitive, usually in a complex waySubject to unpredictable drift (needs frequent recalibration)


No gravity correction requiredVery smallLow power consumptionInsensitive to orientation, motion, and shock; very portableEasily automated

Barometer ComparisonHypsometer characteristics

Extreme non-linearityBest sensitivity at low pressureEasy to calibrateRequires very accurate temperature sensor


Requires very accurate temperature sensorSensitive to orientation, but reasonably portableNo gravity or temperature correctionEasily automated

Let’s make an instrument: Manometer - UNC A pressure Pressure relative ... Absolute Gauge...

Documents

Transcript of Let’s make an instrument: Manometer - UNC A pressure Pressure relative ... Absolute Gauge...