Pressure measurement

MITESH KUMARRall no-10300513026

Applied Electronics & Instrumentation Engg.Haldia Institute Of Technology

Density

D=M⁄VSo for greater density mass will more in the substance in unit volume. And greater density will give more hydrostatic(head) pressure than lower density.Density always define in given temperature because density of a liquid decreases as temperature increases.This temperature is here reference temp.

Specific gravity

• Some time density can define in terms of Specific gravity.

• Specific gravity is the ratio of the density of a particular liquid to the density of water at a reference temperature.

problem: Water has a density of 1,000 kg/m3 at 50 °F. The density of gasoline is 660 kg/m3 at 50 °F. calculate Specific gravity of gasoline?

• Ullage Pressure is pressure that is exerted on the surface of a liquid.• In an open tank, atmospheric pressure (the pressure exerted by the

Earth’s atmosphere) is the pressure on the surface.• A gauge pressure measurement is sufficient for level measurement.• In a closed tank, it is common practice to fill the vapor space with

buffer gas. This is done in order to protect the products inside thetank or to prevent them from evaporating into atmosphere.

• This buffer gas will exert a pressure on the column of liquid thatmust be subtracted from the measurement of the height of theliquid column otherwise error will occur.

• Differential pressure measurement, where the low side referenceleg is connected to the vapor space will allow the head pressure tobe subtracted out.

Ullage Pressure

Factors for gas

• Factors for gas’s exert pressure ⇨ Gas container volume

⇨ Gas temperature.

There is ideal gas law relating it’s pressure temperature and volume.PV= nRT

Relations between gas pressure and volume

Boyel’s law : It is stated that that the pressure and volume of a gas have an inverse relationship, when temperature is held constant. P1V1= P2V2 A fixed amount of gas is transferred to a larger container, the pressure will decrease in proportion to the increase in container volume.

So we can conclude that gas can be compressed, the pressure of a gas increases proportionately as the volume of the container in which it is held decreases.

Need of pressure measurement • There are four common need

⇨ Safety⇨ Process efficiency⇨ Cost savings⇨ Measurement of other process variables

Safety • Pipes, tanks, valves, and other equipment used with pressurized fluids in process industries are designed to withstand the stress of a specific range of pressures.

• Accurate pressure measurement and precise control help prevent pipes and vessels from bursting.

• In addition, pressure measurement and control help minimize equipment damage, reduce the risk of personal injury, and prevent leaks of potentially harmful process materials into the environment.

• Pressure measurement used to control the level and flow of process materials helps to prevent backups, spills, and overflows.

• By monitoring the pressure in the process, actions can be taken to prevent (or minimize) an environmental release or personal injury/ exposure.

Cost saving• The equipment used to create pressure or vacuum in

process industries (e.g., pumps and compressors) uses considerable energy.

• Because energy costs money, a precise pressure measurement can save money by preventing the unnecessary expense of creating more pressure or vacuum than is required to produce required result.

Process efficiency Most common example making paper from paper bulb.

The piece of paper on which these words are written was created from a pulp solution gone through a paper machine at a specific pressure , If the pressure had gone above or below the set point (required range), the result would have been scrap instead of a usable sheet of paper.

So, The efficiency of a process is directly related to the quality of the product being produced.

Measurement of other variables

Pressure transmitters are frequently used to measure..

⇨ Temperature measurement Level of fluid in a tank⇨ Flow rate measurement through a pipe⇨ Density of a substance⇨ ⇨ Liquid interface measurement

Types of pressure measuring sensors

• Mechanical type Instruments⇨ Manometers- Comparing the unknown to known pressure.⇨ Metal diaphragm or bellows or capsules⇨ Bourdon tubes.• Electro-mechanical type Instruments • Vacuum sensors.

U-Tube Manometer

Explanation • Let the density of the fluid whose pressure being measured be ρf and that of

the manometer liquid be ρm.• Equilibrium of the manometer liquid requires that there be the same force

in the two limbs across the plane AA.• We can write : P+ ρfgh= Pa + ρmgh• Finally ,

P-Pa =(ρm- ρf )gh

for manometer liquid most commonly used liquid is mercury(Hg) and basically used for high pressure measurement2nd common liquid is water and basically used for low pressure.

Contd..• When measuring pressures close to the atmospheric pressure in

gases, the fluid density may be quite negligible in comparisonwith the manometer liquid density.

• Rewriting : P – Pa≈ ρm gh

for mercury manometer : ρm=13600kg/m3 ρf=1kg/m3

Contd..Advantages :

• Manometers include simple and time proven construction.• High accuracy.• Good repeatability. • Wide range of filling fluids and use as primary standard or as working device.

Disadvantages :• Include lack of portability.• Need of leveling, the hazardous condition existing when

mercury is used as the filling fluid and exposed to the atmosphere and the reading error due to the meniscus on small diameter tubes.

Well type Manometer• Sometimes a well type manometer is used and it operates in the

same manner as the U-tube manometer, except that construction.

• In the well type manometer, one of the legs of the U-tube is substituted by a large well such that the variation in the level in the well will be negligible and instead of measuring a differential height, a single height in the remaining column is measured.

• The advantage of the well type design is that relatively large pressure differences may be measured with enough manometer liquid being available for doing so.

Contd..

Well type inclined manometer

In case the measured pressure difference is small one may use an inclined well type manometer

Summary Advantages :• Very simple • No calibration required.Disadvantages :• slow response – for fluctuating pressures not useful, useful only for slow

varying pressures.• For the "U" tube manometer two measurements must be taken

simultaneously to get the h value. This may be avoided by using a tube with a much larger cross-sectional area on one side of the manometer than the other.

• For very accurate work the temperature and relationship between temperature and density of the manometric liquid must be known.

Elastic type pressure sensors

Elastic members are also used for measurement of pressure up to 700 MPa.⇨ Bourdon tube or pressure spring.⇨ Bellows elements⇨ Diaphragms.Bellows and Diaphragms can be useable up to 3-6 Mpa but bourdon tubes for very high range.

Bourdon tube • Bourdon tube pressure gages are extensively used for local

indication and signal transmission to remote location.• There are three types of bourbon elements ⇨ c-Type ⇨ spiral ⇨ Helical

C-type• Bourdon gages are purely mechanical devices utilizing the

mechanical deformation of a flattened but bent tube.• The motion is against a spring torque such that a needle

attached to the shaft indicates directly the pressure difference.

C- Type working The Bourdon tube is a metal tube of elliptic cross

section having a bent shape.• The inside of the tube is exposed to the pressure to be

measured. The outside of the Bourdon tube is exposed to a second pressure, usually the atmospheric.

• The Bourdon tube is held fixed at one end (the end connected to the pressure source) and the other end is connected by linkages to a spring restrained shaft.

• A pointer is mounted on the shaft. The needle moves over a circular scale that indicates the pressure.The position of the needle is determined by a balance between the Bourdon tube developed torque acting on the shaft and the torque due to the shaft mounted spring that opposes its movement.

Note

• The commercial Bourdon pressure gauges have near elliptical cross section and tube generally bend into a C- shape or arc length of about 27 degrees.• The materials used are commonly Phosphor Bronze, Brass andBeryllium Copper

Parts of Bourdon tube

Contd..

Mounting position

sensitivity

Spiral type The spiral bourdon element is used when the free-end movement

of the C-type is not great enough to provide the needed motion.

• Since greater movement of the free end is attained with thespiral element, it is not necessary, in most cases, for mechanicalamplification, so better accuracy is obtained.• Spiral tubes are made by winding the tube with its flattenedcross section in a spiral form of several turns.• As pressure is applied to the spiral, it tends to uncoil, producingthe relatively long movement of the tip end whose motion can beused for indication or transmission.

Contd..

Helical type The helical bourdon element is similar to the spiral element,

except it is wound in the form of a helix.• It increases the tip travel considerably, producing even greateramplification than the spiral element.• Usually a central shaft is installed within the helical element,and the pointer is driven from this shaft is installed within thehelical element, and the pointer is driven from this shaft byconnecting links.• This system transmits only the circular motion of the tip to thepointer and hence, is directly proportional to the changes in thepressure

Contd..

Need for various type

• The types are varied for specific uses and space accomodations,for better linearity and larger sensitivity.

• How ? The displacement of the tip varies inversely as the wall

thickness and depends upon cross-sectional form of the tube. But importantly length of the arc. Therefore displacement of the of the tip may be increased by increasing the length of the arc of the tube without changing the wall thickness.

Factors need to consider

• Nonlinearity• Hysteresis• Static error• Elevation error

Non linearity• Because of the compound stresses developed in the tube, actual

tip travel is nonlinear in nature.• However for a small travel of this can be considered to be linear and parallel to the axis of the link.• The small linear tip movement is matched with a rotational pointer movement.• This is known as multiplication, which can be adjusted by adjusting the length of the lever. A shorter lever gives larger rotation for the same amount of tip travel.• The approximately linear motion of the tip when converted to a circular motion with a link-lever and pinion attachment, a one-to one correspondence between them may not occur and a distortion results. This is known as angularity which can be minimized by adjusting the length of the link

Hysteresis , Static error and Elevation error

•Hysteresis:• Like all elastic elements Bourdon tube element also has somehysteresis in a given pressure cycle. By proper choice ofmaterial and its heat treatment, this may be kept low.• Static error:• It generally appears because of the change in elasticity due tochange in temperature. With temperature rising, elasticitydecreases and hence, indication would increase.• Materials like Ni-span C, which consists of highest amount of Ni.Lowest amount of carbon is virtually free from this change andhence is suitable for low static error.• Elevation error occurs if the tubing connecting the pressuremeasuring element and the pressure point is partially filled

Advantages and Disadvantages

• Simple construction • Very low cost • Improved design at high pressure for maximum safety⇨ Disadvantages :• They are susceptible to shock and vibration due to their

large overhang.• They are subjected to hysteresis

Dead Wight tester

working• A Bourdon pressure gage may be calibrated by the use of a deadweight tester, a schematic of which is shown in Figure.• The dead weight tester consists of an arrangement by which apiston may be allowed to float over a liquid (usually oil) underinternal pressure and a force in the opposite direction imposedon the piston by weights placed as indicated in the figure.• The oil pressure is changed by the pumping piston. The pressureis calculated as the weight placed on the piston divided by thecross section area of the piston (the piston is to be orientedwith its axis vertical).• The gage under test experiences the same pressure by beingconnected to a side tube communicating with the oil.

limitations

• The fiction between the cylinder and the priston.

• The uncertainty in the area of the priston

Typical dead weight tester supplied by WIKA, Australia