Pressure Measurement

Ashish J. ModiLecturer, Dept. of Mech.Engg.,

Shri S.V.M. inst. Of Technology, Bharuchhttp://www.ashishjmodi.synthasite.com

Manometers

Sensors, Transducers

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PressurePressure•

Pressure is a force per unit area exerted by a fluid perpendicular (say normal) to a boundary (as opposed to shear stress, which is exerted parallel to the boundary.)

•

A more precise term is hydrostatic pressure.

•

Since almost all pressure sensors measure a pressure difference, we need to distinguish between absolute and gauge pressures.

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Units of Measure

System Length Force Mass Time Pressure

MKS Meter Newton Kg SecN/M2 =Pascal

CGS CM Dyne Gram Sec D/CM2

English Inch Pound Slug Sec PSI

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STANDARDS

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Atmospheric Pressure

(Pat

):This is the pressure exerted by

envelope of air surrounding the earth’s surface.

Usually determined by Mercury column barometer.

But Mercury has a low vapour pressure (≈1.6×10-6kg/cm2 at 20ºC

)

Terminology

ghPP vpat

ghPat

Pat

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Absolute Pressure

(Pabs

): Pressure has been defined as the force per unit

area due to interaction of fluid particles amongst themselves.

A zero pressure intensity will occur when molecular momentum is zero. Such situation can occur only when there is a perfect vacuum.

Pressure intensity measured from this state of vacuum or zero pressure is called absolute pressure.

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Gauge Pressure

(Pg

) and Vacuum

(Pvac

):When the unknown pressure is more than

atmospheric pressure, the pressure recorded by the instrument is called gauge pressure.

A pressure below the atmospheric pressure is known as vacuum, negative pressure.

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How is pressure generated?

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Collision of molecule with wall•

Momentum is mass x velocity

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Change of momentum is double•

Collision is isothermal = perfectly elastic

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Sum collisions over area to get force

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How is pressure measured?

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Absolute Vs. relative pressure•

Manometry

•

Bourdon•

Aneroid

•

Strain gauge

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The hydrostatic pressure at any point in a fluid is related to the pressure at any other point by the weight of the fluid between the two points.

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Two points at the same elevation in a continuous fluid at rest are at the same pressure, calle

d Pascal’s law,

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Pressure applied to a confined fluid increases the pressure throughout by the same amount.

•

In picture, pistons are at same height:

•

Ratio A2

/A1

is called ideal mechanical advantage

1 2 2 21 2

1 2 1 1

F F F AP PA A F A

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Pressure Reference Instruments•

Reference instruments are those which utilize directly the weight of a column of fluid. Pressure can be calculated from the geometry of the instrument and the specific weight of the fluid.

•

They can be made quite precise but do not generally provide an electrical output.

•

The most common instrument is the manometer, which measures a difference between two pressures

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•

Manometers can be used to measure gauge, differential , atmospheric and absolute pressure –

e.g., Piezometer U-tube manometer –

(single & Double column)

U-tube differential manometerU-tube single reservoir manometerU-tube double reservoir manometerInclined tube manometer

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Piezometer Tube

Force balance : pA(abs) + 1 h1= po

pA (abs)

Closed End “Container”

po

Rearranging: 11hpp oA Gage Pressure

Then in terms of gage pressure, the equation for a Piezometer Tube:

1) The pressure in the container has to be greater than atmospheric pressure.

2) The measurement of pressure must be of a liquid.

Note: pA = p1 because they are at the same level

Gage Pressure,

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The Manometer

• An elevation change of z in a fluid at rest corresponds to P/g.

• A device based on this is called a manometer.

• A manometer consists of a U-tube containing one or more fluids such as mercury, water, alcohol, or oil.

• Heavy fluids such as mercury are used if large pressure differences are anticipated.1 2

2 atm

P PP P gh

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•

The static sensitivity K can be controlled within limits by selecting the manometer fluid, although the density of most gases at atmospheric pressure is much less than that of any liquid.

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U-Tube

ManometersU-Tube

Manometers

• Examples of U- Tube Manometers are as follows:

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How can you measure the pressure?

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Manometer

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Manometer–

measures contained gas pressure

U-tube Manometer

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We can also increase the static sensitivity by using a micro- manometer, which improves the precision of measuring H.

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Another technique which increases static sensitivity is inclining the sensing tube.

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U-tube Manometer

http://hyperphysics.phy-astr.gsu.edu/Hbase/fluids/flupic/bern5.jpg

Air Water Manometer

http://www.armfield.co.uk/images/H12.gif

Mercury Water Manometer

Applications: air pressure, pipe pressure, etc.

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Advantages and Disadvantages of Manometers

Advantages:•

Linear

•

No calibration required•

Good precision

•

Relatively InexpensiveDisadvantages:•

No electrical output

•

Poor Sensitivity•

Poor Dynamic Response.

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The Barometer• Atmospheric pressure is measured

by a device called a barometer; thus, atmospheric pressure is often referred to as the barometric pressure.

• PC can be taken to be zero since there is only Hg vapor above point C, and it is very low relative to Patm .

• Change in atmospheric pressure due to elevation has many effects: Cooking, nose bleeds, engine performance, aircraft performance.

C atm

atm

P gh PP gh

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Barometer

(a) (b) (c)

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Barometer•

It measures the difference between ambient pressure and the vapor pressure of mercury (at 25o C, the vapor pressure is .002 mmHg, which is about 10-4 atm).

•

If ambient temperature is measured, the result can be corrected for the vapor pressure as well as the dependence of specific weight on temperature.

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They are used to calibrate other pressure transducers. They are null rather than deflection instruments.

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•

The primary error in their use comes from friction between the piston and cylinder.

•

This can be minimized by spinning the piston during the measurement (dynamic friction is less than static) and by proper design.

•

The clearance between piston and cylinder must be small enough to prevent leakage but large enough to limit friction.

•

The pressure is therefore,

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Pressure Transducers •

Almost all pressure transducers operate on the basis of elastic deflection - the applied pressure causes some component to deform or deflect.

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Pressure Measuring DevicesBourdon Gage:

http://www.hydraulicspneumatics.com/FPE/images/sensors1_1.jpg

Applications: tire pressure, pressure at the top or along the walls of tanks or vessels

http://www.cpigauges.com/images/gauges/WeldGageStlCsBM400psi.jpg

Principles: change in curvature of the tube is proportional to difference of pressure inside from that outside the tube

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The Bourdon Tube

The Bourdon Tube forms the basic element of most dial pressure gauges.

Static sensitivity can be controlled by varying the dimensions of the tube.

It is possible, though not common, to convert the mechanical output to an electrical signal by bonding strain gages to the tube.

Bourdon tube gages can be made quite precise by using large diameter dials.

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Typical pressure sensing Element

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The Bourdon Tube

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The Bourdon Tube

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•

Bellows and capsule elements are frequently used when an electrical output is desired.

Bellow and Capsule Gauge

Bellow type Capsule type

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Bellow Gauge

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Other Electrical Pressure Transducers

•

What is a pressure transducer?–

A pressure transducer is a device that converts a pressure signal to an electric signal.

•

What type of devices can be used to create a pressure transducer?

•

Strain gage devices•

Capacitance devices

•

Piezoelectric devices

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Pressure Transducer Strain gage device

Strain gage is attached to a flexible membrane. When the membrane is deflected the resistance in the strain gage changes.

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Strained Gauge Sensors

A strain gauge measures the strain in a material subjected to applied stressSignal due to deformation of the material is small, on the order of 0.1% of the base resistance.

Used a metal diaphragm with strain gauges bonded to it.

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Widely used, both bonded and integrated into a silicon diaphragm, because larger (one order of magnitude) response than metallic strain gauge.

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Piezoresistive

effect: Change of resistance, when the crystal lattice structure of silicon is deformed by applied stress.

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Electrical readoutCross-coupling with temperature

Apply several gauges and use Wheatstone bridge

Signal enhanced, Temperature effect strongly reduced

tension

compression

Two more gauges on the other side

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Diaphragm elements are the most commonly used transducers with an electrical output.

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Diaphragm Gauges

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Pressure Transducer Capacitance device

The capacitance between two plates changes with the distance between the plates.

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Pressure Transducer Piezoelectric device

Piezoelectric device take advantage of the electrical properties of crystals such as quartz. These crystals generate an electrical charge when they are strained.

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