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McLeod Gauge is a vacuum gauge that uses the same principle as that of a manometer. By using the pressure dividing technique, its range can be extended from a value of 10-4 Torr. The basic principle is called the multiple compression technique. It is shown in the figures below. If there are two bulbs A and B connected with the McLeod and test gauges through capillary tubings, the pressure on the right hand side of the test gauge is very small and the capillary connection between T and bulb B very long, then the flow law can be written as

V.dp2/dt = K.(p1-p2)

V- Volume of the bulb

dp2/dt – Pressure Gradient in time between the two elements

K – Flow conductance in the capillary.

As p2 is very small when compared to p1, the flow rate remains practically constant and is proportional to the pressure. This forms the basis of the calibration.

There are many variations of the McLeod Gauge. The basic construction is shown in the figure below.

McLeod Gauge

Working

The gauge is used to compress a small quantity of low pressure gas to produce a readable large pressure. Bulb B of the gauge is attached to capillary aa’. The mercury level in the gauge is lowered up to l1 by lowering the reservoir, thereby allowing a little process fluid to enter B. By raising the reservoir, the gas is now compressed in the capillary aa’ till mercury rises to the zero mark in the side tube and capillary bb’. The capillary bb’ is required to avoid any error due to capillary.

The McLeod gauge is independent of gas composition. If, however, the gas contains condensable material and during compression it condenses, the reading of the gauge is faulty. The gauge is not capable of continuous reading and the scale is of square law type. For linearizing the scale at comparatively higher pressures, a second volume is introduced as shown in the figure below, where the scale shown is linear.

McLeod Gauge For Linear Scale

For pressure measurement below atmosphere or vacuum, different gauges are available. Manometers and bell gauges can go up to 0.1 Torr. Diaphragm gauges are usable up to a pressure of 10-3 Torr. For pressure below this value, electrical gauges like Pirani or Ionization Gauges are used. Vacuum measurement is broadly classified into Mechanical Type, Thermal Type, Ionization Type, and Radiation Vacuum Gauge.

Thermal Types

The heat conductivity of gases is independent of its pressure, at normal pressure. But, heat conductivity starts falling as the pressure is lowered t 10 Torr and below. The reason behind this is less collision between gas molecules within the wall and also their small number in a specific volume. The energy is carried to the walls of the container due to this collision. Thus, lesser number of molecules will be available to take the heat away from the source.

At low pressures, the heat loss that occurs from a hot wire mounted in a glass or metal tube is due to the following factors.

• Convection
• Conduction through the lead mines
• Conduction in the gas

Out of these, convection is comparatively negligible. A new clear wire has a small surface emissivity and is god for producing high temperature at low gas pressures. Due to oxidation and carbonization, the surface tends to deteriorate. This causes error of the device at low pressure ranges.

Optical type pressure measurement is receiving considerable attention in recent years where the movement of a diaphragm, a bellows element or such other primary sensors are detected by optical means. The principle is nothing new, but the technique of adaptation in commercialization is varied in nature. A typical case with a diaphragm and a vane attached to it that covers and uncovers an irradiated photo diode with changing pressure is shown in the figure below.

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Optical Type Pressure Sensor

The circuit diagram shows that if any instant uncovering area of the photo diode is Am, and that of reference one is Ar, with other notations shown in the figure, the ratiometric output would be

Vf/VR = G(Am/Ar – a)

Calibration may be made directly in pressure. The ratiometric technique is often preferred for avoiding drift error in electronic components as they are likely to be equally affected and cancelled. The vane movement or the diaphragm movement is kept small for negligible hysteresis and good precision. Diode signals have non-linearities which may also vary from unit to unit. The non-linearities are often linearised using look up table in programmable read only memories during A/D conversion process. The range may be adjusted from (0-400)MPa with an accuracy of 0.1 percent scan. Temperature, though compensated, affects measurement to a certain extent which, in zero scale may be compensated by auto-zeroing facility.

This system is often used as a null detecting one in a force balance type pressure measurement, where the servo-system brings the sensor to the zero balance point.

Resistance Strain Gauges can be used as a secondary element in pressure measurement. They can be joined together with bellows and diaphragms to effectively measure pressure. The figures below show the scheme of a differential pressure measurement.

The figure below shows the arrangement of strain gauges that are mounted on a cantilever spring which is operated by a pair of opposing bellow elements. The cantilever is properly chosen in dimension for compensation in the change in the Young’s modulus due to temperature changes.

Pressure Measurement With Strain Gauge on Bellows

The figure below shows an arrangement if strain gauges on to a flat diaphragm. Usually four gauges are   mounted as shown and they are connected in a bridge circuit as shown in the figure. Radial and tangential stresses are developed in the diaphragm gauges complicating the measurement of true pressure.

Pressure Measurement With Strain Gauges on Diaphragm

In recent years miniaturization is effected where the discrete gauges are replaced by a rosette which is available in various sizes. The rosettes may be configured such that the radial strains at the edge of the diaphragm and tangential strain near the centre are easily picked up while the solder points/tabs are located in a low strain region.

Unbounded strain gauges can also be adopted for measuring strain and in consequence pressure with a diaphragm. A simple schematic of such a pressure measurement is shown in the figure below. Emperical calibration for all the above cases is always preferred.

Pressure Measurement Using Unbonded Strain Gauges

Capacitance Transducer

A capacitance pressure transducer is based on the fact that dielectric constants of liquids, solids and gases change under pressure. The figure below shows an arrangement of a cylindrical capacitor that can withstand large pressure. As the change in dielectric constant is quite small (only about ½ percent change for a pressure change of about 10 MPa), it is usable only at large change in pressure. Besides, the capacitance-pressure relation is non-linear and is affected by temperature variation. The measurement of this capacitance is done by a resonance circuit. The schematic is shown below. The oscillogram giving the variation of the output voltage with capacitance is also shown below.

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Pressure Measurement by Change in Dielectric Constant Using Resonance Circuit

Capacitive Transducer

A basic capacitive transducer has already been explained (Refer: Capacitive Transducers). It consists of a pair of parallel plates with the middle plate moving with pressure and producing a differential capacitor system. The figure below shows a pressure gauge of this type. Spherical depression of the glass plate is less than 0.0025 centimetres. When a differential pressure exists, the thin steel diaphragm moves towards the low pressure side and the output voltage e0 measured as the difference of voltage e1 and e2 across the two capacitors formed with this movable plate is given by the equation

e0 = e1-e2 = Ex/d

x – Displacement of the diaphragm

d – Diameter

Capacitive Pressure Transducer

Such transducers are frequently used in pressure transmitter.

As fibre-optic type pressure measurement is versatile in many applications fields, it is gradually becoming popular. Its adaptability in bio-medical area has also been confirmed in which case, it can be used to monitor pressure in the human circulatory system. The basic diagram of the system is shown below.

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Fibre Optic Type Pressure Measurement System

There are two optical fibre bundles called guides – input and output – arranged as shown in the end view, giving the proper perspective. Chopped light from source is focused on to input guide, which on emergence is reflected from a flexible membrane. The membrane may be made of aluminized plastic formed as a film. With pressures, P1 and P2 equal, the position of the membrane with respect to the input guide is so kept that 50% of the reflected light falls on the surrounding annular output guide. With P2 greater than P1, the membrane becomes convex towards the guides and more light falls on the output guide, while with P1 less than P2, the reverse occurs. A detector set at the other end of the output guide correspondingly receives varied amount of light with changing pressure. The detector can be calibrated for pressure.

A surface acoustic wave (SAW) delay line, consisting of two inter-digital transducers (IDT) when stretched along the propagation direction or bent as a cantilever beam, its substrate becomes stressed causing an elongation of the substrate, in turn, causing an increase in the centre-to-centre distance between the two IDT’s. High stress also changes the material and its elastic constants causing the velocity Vs of the surface acoustic wave to change. This change can also be brought by change in temperature, pressure, force, and the delay line can thus be used as sensors for temperature, pressure, force, displacement, and so on.

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One method of using the delay line as a practical sensor is to introduce it in the feedback path of an amplifier to obtain an oscillator with its frequency as a function of the stress. The figure is shown below.

Surface Acoustic Wave (SAW) Sensor

As in most devices, temperature affects the performance by changing the property of the material. However, every quartz crystal cut appropriately has a turnover temperature at which the effect of temperature is minimum. Also, if surface wave is proportional on both faces of the substrate using two pairs of IDT’s, the sensitivity increases and effect of temperature is reduced.

There are mainly three types of electrical pressure transducers – inductive, resistive, and capacitive. The inductive type consists of a Linear Voltage Differential Transformer (LVDT) where core is positioned by the pressure through a diaphragm or a bellows element as shown in the figure below.

The same method can be extended to develop a null-balance type instrument as shown in the figure below. Feedback through the force coil produces the wanted balance while the output is taken across resistor R and is of value K*(p1-p2), K being a constant.

LVDT Type Electrical Pressure Transducer

Some of the most commonly used electrical pressure sensors are:

A high accuracy stable pressure transducer often recommended as calibration standard for gas pressure and density, is obtained by making a thin walled cylinder oscillate continuously in one of its vibration modes – specifically circumferential mode using limit cycle feedback system. Any change in the pressure causes change in the oscillation frequency and the reluctance type pick-up cum drive system produces an output signal which is processed and displayed by electronic means. Provision for temperature compensation is also made where a solid state temperature sensor picks up temperature change and a microprocessor system makes the relevant compensation.

In resistive pressure transducers, the pressure operates the primary sensors as in a bourdon tube, a diaphragm or a bellows element or even the liquid column in a manometer. The mechanical movement of this primary sensor is then converted into electrical signals by resistance variations as shown in the figures below. Figure (4) shows a liquid contact type resistance pressure gauge where with increasing pressure more and more resistances are shortened and the resistance R is decreased. A current meter will directly indicate the pressure.

Electrical Pressure Transducers – Working, Construction

The modified system is shown in the figure below where a resistance ratio element is used. Long resistance wires are introduced into two manometer legs containing a conducting fluid. The unbalance current in galvanometer directly indicates the pressure difference (p1-p2).

Resistance Ratio Element Gauge

Bridgeman Pressure Gauge

When a wire is subjected to pressure from all sides its electrical resistance changes. This principle can be utilized to obtain a primary type resistive pressure sensor and is called as a Bridgeman pressure sensor. The distortion produced in the crystal lattice due to the external pressure causes the change in resistance. In most common metal wires, the resistance decreases with increase in pressure, while for antimony, bismuth, lithium, and manganin, it increases. In cesium, it initially decreases for small values of pressure changes and reaches a minimum, beyond which it increases with increase in pressure. But these metals cannot be used for practical purposes in a bridgeman gauge. The gauge must be used at a constant temperature, and has a range from 0 to 1000 MPa, but usable only at high pressure, as, at low values of pressure the change in resistance value is very small because of the small value of the pressure co-efficient of resistance.

The constructional features of bridgeman gauge has improves since it was first proposed. The basic construction is shown in the figure below. It has a bone ring shape with an insulated manganin wire having a pressure co-efficient of resistance of 23×10-7 cm2/kg so that the total resistance of the wire is 100 ohm. The winding is generally bifilar for avoiding inductive effect. Carbon can also be used for pressure measurement in the form of granules or discs. With pressure, its resistance also changes, but non-linearly and is not suitable for a linear scale measurement. The carbon resistance pressure gauge diagram is shown below.

Bridgeman Gauge

A diaphragm pressure transducer is used for low pressure measurement. They are commercially available in two types – metallic and non-metallic.

Metallic diaphragms are known to have good spring characteristics and non-metallic types have no elastic characteristics. Thus, non-metallic types are used rarely, and are usually opposed by a calibrated coil spring or any other elastic type gauge. The non-metallic types are also called slack diaphragm.

Working

The diagram of a diaphragm pressure gauge is shown below. When a force acts against a thin stretched diaphragm, it causes a deflection of the diaphragm with its centre deflecting the most.

Diaphragm Gauge

Since the elastic limit has to be maintained, the deflection of the diaphragm must be kept in a restricted manner. This can be done by cascading many diaphragm capsules as shown in the figure below. A main capsule is designed by joining two diaphragms at the periphery. A pressure inlet line is provided at the central position. When the pressure enters the capsule, the deflection will be the sum of deflections of all the individual capsules. As shown in figure (3), corrugated diaphragms are also used instead of the conventional ones.

Diaphragm Pressure Transducer

Corrugated designs help in providing a linear deflection and also increase the member strength. The total amount of deflection for a given pressure differential is known by the following factors:

• Number and depth of corrugation
• Number of capsules
• Capsule diameter
• Shell thickness
• Material characteristics

Materials used for the metal diaphragms are the same as those used for Bourdon Tube.

Non-metallic or slack diaphragms are used for measuring very small pressures. The commonly used materials for making the diaphragm are polythene, neoprene, animal membrane, silk, and synthetic materials. Due to their non-elastic characteristics, the device will have to be opposed with external springs for calibration and precise operation. The common range for pressure measurement varies between 50 Pa to 0.1 MPa.

The best example for a slack diaphragm is the draft gauge. They are used in boilers for indication of the boiler draft. The device can control both combustion and flue. With the draft, usually of pressure less than the atmosphere, connected, the power diaphragm moves to the left and its motion is transmitted through the sealing diaphragm, sealed link and pointer drive to the pointer.

The power diaphragm is balanced with the help of a calibrated leaf spring. The effective length of the spring and hence the range is determined by the range adjusting screw. By adjusting the zero adjustment screw, the right hand end of the power diaphragm support link as also the free end of the leaf spring, is adjusted for zero adjustment through the cradle.

Like a diaphragm, bellows are also used for pressure measurement, and can be made of cascaded capsules. The basic way of manufacturing bellows is by fastening together many individual diaphragms. The bellows element, basically, is a one piece expansible, collapsible and axially flexible member. It has many convolutions or fold. It can be manufactured form a single piece of thin metal. For industrial purposes, the commonly used bellow elements are:

• By turning from a solid stock of metal
• By soldering or welding stamped annular rings
• Rolling a tube
• By hydraulically forming a drawn tubing

Working

The action of bending and tension operates the elastic members. For proper working, the tension should be least. The design ideas given for a diaphragm is applied to bowels as well. The manufacturer describes the bellows with two characters – maximum stroke and maximum allowable pressure. The force obtained can be increased by increasing the diameter. The stroke length can be increased by increasing the folds or convolutions.

For selecting a specific material for an elastic member like bellows, the parameters to be checked are:

• Range of pressure
• Hysteresis
• Fatigue on dynamic operation
• Corrosion
• Fabrication ease
• Sensitivity to fluctuating pressures

Out of these hysteresis and sensitivity to fluctuating pressures are the most important ones. Hysteresis can be minimized by following a proper manufacturing technique. For instance, a diaphragm when machined from a solid stock shows less hysteresis compared to the one produced by stamping. The same technique could be adopted for bellows as well. In the latter case, the dynamic nature of the variable is likely to induce resonance quickly depending on the natural frequency of the system. The natural frequency is calculable from the dimensions of the system and the gauge.

For strong bellows, the carbon steel is selected as the main element. But the material gets easily corroded and is difficult to machine. For better hysteresis properties you can use trumpet bass, phosphor bronze, or silicon bronze. Better dynamic performance can be achieved by using beryllium copper. Stainless steel is corrosion resistive, but does not have good elastic properties. For easy fabrication soft materials are sought after.

All bellow elements are used with separate calibrating springs. The springs can be aligned in two ways – in compression or in expansion when in use. Both these types, with internal compression springs or external tension springs, are commercially known as receiver elements and are used universally in pneumatic control loops. The figures below show the compressed and expanded type. Spring opposed bellows are also shown below. The open side of a bellows element is usually rigidly held to the instrument casing and because of the rigid fixing, the effective or active length of the bellows element is smaller than its actual length. This device is used in cases where the control pressure range is between 0.2 to 1 kg/cm2.

Bellow Pressure Gauge

Because of the device’s dynamic operation, the life of a bellow is an important consideration. Nomograms are available with the manufacturers, wherefrom the life in circles can be read directly knowing the per cent maximum pressure and per cent maximum stroke.

In terms of choice of elastic material for the sensors, the corrosive medium requires special precaution. Besides this, there are other factors showing that the medium should not come in direct contact with the measuring element. They are shown below:

• The direct impact of static head on the measuring element may cause error in response.
• Direct touch of the medium may cause corrosion, high viscosity fluids may cause response error and entrailed materials in the medium may clog in the element.
• In some critical processes in food processing and pharmaceutical industries, cleaning of the measuring system is necessitated.
• Removal of the measuring element for servicing should be convenient.

All these factors suggest that a type of seal should be placed between the process fluid and the measuring element. The best example is the diaphragm seal. It consists of a flexible diaphragm made of corrosion resistance material and sealed within a chamber, that can connect the process on one side and the measuring element on the other.

The effective area of an elastic element like diaphragm or bellows element is generally less than the geometrical area. For finding out the effective area, a known load change is made externally o the centre of the element and the corresponding deflection noted. The differential pressure is then found out for the same deflection.