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Demos: U-tube manomoter, Archimedes principle, const fluid height, venturi flowmeter. . Lecture 7. Mechanical sensors: motivations. How do we predict materials failure? . Strength is the ability to withstand force or stress. Predict cracks and collapse in bridges and buildings.

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Lecture 7

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Mechanical sensors: motivations.

How do we predict materials failure?

Strength is the ability to withstand force or stress

Predict cracks and collapse in bridges and buildings

Aircraft wings (DC-10 metal fatigue: the wings suddenly fell off)

Remember stress=force/area


How do we measure fluid flow?

Usually want laminar flow, not turbulent.

Beer taps-want to avoid losing the bubbles

Grain silos-want to predict the rate of static buildup to avoid explosions, yet maximize the throughput

Chemical reactions-want to ensure fluids properly mixed


Blood/brain/spinal fluid pressure-how do we measure non-invasively?

How do we measure hydrostatic pressure in fluids and liquids?

Hydraulic systems-bulldozer arms, car disk brakes/hydraulic lifts

How do divers know how much air they have left in their tanks?


Pressure sensors:

How do we tell when someone is walking down a corridor?

How can we weigh trucks as they pass over a road?

mechanical sensors
Mechanical Sensors
  • Definitions
  • Force and pressure sensors
  • Basic pressure sensors
  • Medical pressure measurement systems
  • Flow and flow-rate sensors.

In this section of the course, we will cover:

What defines a mechanical sensor? It reacts to stimuli via some mechanical effect.

The output may be

Mechanical (e.g. a dial or fluid level) or Electrical (e.g. a voltage or current)

force and pressure sensors
Force and Pressure Sensors

How do we measure an unknown force?

Acceleration Method

Example: Force on Pendulum, apply force measure deflection.

Apply force to known mass, measure acceleration.

force and pressure sensors8
Force and Pressure Sensors

Gravity balance method.

Compare unknown force with action of gravitational force.

Example: Balance scale. (zero-balance method)


Spring Method

Use force to stretch or compress a spring of known strength, and measure displacement: F=kx , k is the spring constant.

Example: Fruit scales at supermarket


Pressure-sensing method.

Convert the unknown force to a fluid pressure, which is converted using a pressure sensor. Also known as deadweight sensor-used for weight calibrations.


Pressure-sensing method.

  • Beer in (untapped) keg
  • Butane gas bottle.
  • Diving tank

If force is constant, pressure is static or hydrostatic:

  • Arterial blood pressure
  • Beer flowing in brewery
  • Lift in aeroplane wings

If force is varying, pressure is dynamic or hydrodynamic:

  • 1 Pascal = 1 Newton/m2
  • 1 atm (Atmospheric pressure) = 101325 Pa
  • 760 torr = 1 atm

Units of Pressure:

Pressure is usually measured relative to some reference.

There are four basic reference configurations:

pascal s principle
Pascal’s Principle

Pressure applied to an enclosed system is transmitted undiminished to every portion of the fluid and container walls.

This is the basis of all hydraulics: a small pressure can be made to exert a large force by changing the dimensions of the vessel

applications of pascal s principle

The bottle bottom breaks when the mouth is struck.

Applications of Pascal’s Principle


Disk brakes

Car Lift

Medical applications

notes on pascal s principle
Notes on Pascal’s principle

Pascal’s principle neglects the effects of gravity-need to add the contribution ρgh where ρ is the density, g the acceleration due to gravity, and h the height of the fluid.

Also, only true in hydrodynamic systems if change is quasi-static.

Quasi-static means that after a small change is made, turbulence is allowed to die down then measurement is made.

Examples are hydrodynamic systems where flow is non-turbulent and the pipe orifice is small compared with its length.

some pressure sensing elements
Some pressure sensing elements

From H. Norton, ‘Sensor and analyzer handbook’

These all convert a pressure into an angular or linear displacement. We can then sense the displacement electronically or optically.

bourdon tube sensor
Bourdon tube sensor

Bourdon tube pressure sensor: curved or twisted tube, sealed at one end.

As pressure inside changes, tube uncurls; this displacement can be transduced using a variable sliding resistior, or linked directly to a dial readout.

membrane pressure sensors
Membrane pressure sensors

Subdivided into bellows, thin plate and diaphragm sensors.

These work by measuring the deflection of a solid object by an external pressure.

This displacement is then measured, and converted into a pressure reading

mems sensors

Mechanical sensors can be made very small using micromachining; called microelectromechanical systems (MEMS).

MEMS sensors
  • 1 μm high MEMs capacitive accelerometer: such devices are at the heart of car airbags.
  • Machined out of single silicon wafer
  • ‘Proof mass’ is freer to move in response to acceleration forces

MEMs gyroscope based on ‘tuning fork’ design-uses mechanical resonance of micromachined structure to determine orientation.

Images from www.sensorsmag.com/articles/0203/14/

medical pressure measurement
Medical pressure measurement.

Most common measurement is for blood pressure. More fully:

This is a major application for sensor technology.

  • Inter-cardiac blood pressure
  • Arterial blood pressure
  • Venous blood pressure
  • Pulmonary artery pressure
  • Spinal fluid pressure
  • Central venous pressure
  • Intraventricular brain pressure

The difference in these measurements is the range of measurement; we can often use the same sensor for different measurements

medical students are often told there is an ohm s law for blood

Medical pressure sensors

Medical students are often told there is an “Ohm’s law for blood”
  • minimally invasive
  • sterile
  • electrically insulated

Medical sensors should be:

  • P is pressure difference in torr.
  • F is flow rate in millilitres/second.
  • R is blood vessel resistance in “periphial resistance units” (PRU) where 1 PRU allows a flow of 1 ml/s under 1 torr pressure.

P=F.R , Where:

This is misleading: in fact, blood vessels change diameter from systemic adjustments and from pulsatile pressure wave.


In fact, the flow rate is better given by Poiseuille’s Law:


  • F is flow in cubic centimetres/second
  • P is Pressure in dynes per square centimetre
  • ηis coefficient of viscosity in dynes/square centimetre
  • R is vessel radius in centimetre
  • L is vessel length in centimetres
blood pressure waveform
Blood Pressure Waveform

Four kinds of pressure:

T2 : Peak Pressure (systolic)

Tf: Minimum pressure (diastolic)

Dynamic Average (1/2 peak minus minimum)

Average pressure (arterial)


mean arterial pressure is given by

Blood Pressure Analysis

Mean arterial pressure is given by:

But clinically (for doctors and nurses in a hospital or sleep lab setting) a much simpler approximation is used:

Where P1 is diastolic Pressure and P2 is systolic pressure

Direct measurement of blood pressure is most accurate but also more dangerous (involves poking tubes into arteries, very invasive.)

open tube manometer
Open Tube Manometer

=density of Manometer fluid

Sensing tube tube inserted directly into artery; mercury is poisonous, so need saline buffer

Measure pressure by height of sensing column:

Only used in intensive care units.

sphygmomanometry korotkoff method
Sphygmomanometry (Korotkoff Method)
  • Inflatable cuff placed on upper arm and inflated until blood can’t flow
  • Sound sensor (stethoscope) placed downstream
  • Pressure is released
  • When can hear blood squirting (Korotkoff sounds), the cuff pressure equals systolic (higher) pressure
  • Hear continuous but turbulent flow when cuff pressure equals diastolic pressure


the diamond anvil
One way to get huge pressures is to use diamonds to squeeze a sample

Can achieve pressures up to 80 GPa (or even higher)

So, like, is that big?

The diamond Anvil


relative pressure scale
Relative pressure scale

Pressures are given in Atmospheres

10-31 |- Non equilibrium "pressure" of hydrogen gas in intergalactic space.

10-28 |-

10-25 |-

10-22 |- Non equilibrium "pressure" of cosmic microwave background radiation.

10-19 |- Pressure in interplanetary space.

10-16 |-Best vacuum achieved in laboratory.

10-13 |- Atmospheric pressure at altitude of 300 miles.

10-10 |- Pressure of strong sunlight at surface of earth.

10-8 |-

10-7 |- Partial pressure of hydrogen in atmosphere at sea level.

10-6 |-Best vacuum attainable with mechanical pump. Radiation pressure at surface of sun.

10-5 |-Pressure of the foot of a water strider on a surface of water. Osmotic pressure of sucrose at concentration of 1 milligram per liter.

10-4 |-Pressure of sound wave at threshold of pain (120 decibels). Partial pressure of carbon dioxide in atmosphere at sea level.

10-3 |- Vapour pressure of water at triple point of water.

10-2 |-Overpressure in mouth before release of consonant p. Pressure inside light bulb.

10-1 |- Atmospheric pressure at summit of Mount Everest.

1 |-Atmospheric pressure at sea level. Pressure of ice skater standing on ice.

10 |-Maximum pressure inside cylinder of high compression engine. Air pressure in high-pressure bicycle tyre.

102 |-Steam pressure in boiler of a power plant. Peak pressure of fist on concrete during karate strike.

103 |-Pressure at greatest depths in oceans.

104 |-Pressure at which mercury solidifies at room temperature. Pressure at which graphite becomes diamond.

105 |-Highest pressure attainable in laboratory before diamond anvil cell. Radiation pressure of focused beam of pulsed laser light.

106 |-Highest pressure achieved with diamond anvil cell. Pressure at centre of Earth.

107 |-Pressure at centre of Saturn.

108 |-Pressure at centre of Jupiter. Radiation pressure at centre of sun.

1010 |- Pressure at centre of sun.

1013 |-

1016 |-Pressure at centre of red-giant star. Pressure at centre of white-dwarf star.

1019 |-

1022 |-

1025 |- Pressure at centre of superdense star.

1028 |- Pressure at centre of neutron star.

the holtz cell
The Holtz cell is a way to achieve huge pressures in a diamond anvil. Uses a simple lever system to apply pressureThe Holtz cell
flow and flow rate
Flow and Flow rate.

Turbulent flow: chaotic phenomena (whorls, eddies, vortices)

Laminar flow: smooth, orderly and regular

Flow in a capillary described by Pouiselle’s law.(But beware: only valid for laminar flow)

Mechanical sensors have inertia, which can integrate out small variations due to turbulence

This begs the question: what makes flow laminar or turbulent?

laminar and turbulent flow
Laminar and Turbulent flow
  • Laminar flow is characterised by :
  • smooth flow lines
  • all fluid velocity in same direction
  • flow velocity is zero at tube walls
  • flow speed increases closer to tube center
reynolds number
Reynolds Number.

Reynold’s Number R


ρis the fluid density (kg/m3)

V is the mean fluid velocity (m/s)

D is the capillary/pipe diameter (m)

 is the viscosity of the fluid (Ns/m2)

R > 4000, flow is turbulent

R < 2000, flow is laminar

flow sensors
Flow Sensors

Many sensors measure flow rate.

Mass flow rate: mass transferred per unit time (kg/s)

Volumetric flow rate: volume of material per unit time (m3/s)

In gas systems, mass and volume rates are expressed in volume flow.

Mass flow referenced to STP (standard temperature and pressure) and converted to equivalent volume flow (eg sccm = standard cubic centimetres per minute)

thermal flow sensor
Thermal flow Sensor

Cooling of resistive element by fluid flow is measured by Voltmeter

Hot wire anenometer:

mass flow controllers

Uses two thermometers which supply heat to the gas as well as measuring temperature

  • The faster that the gas flows, the more heat is removed from the upstream thermometer
  • The downstream thermometer also measures the heat flow, increasing accuracy
  • No contact between sensors and gases (no contamination)
Mass Flow controllers
photo of a mass flow controller
Photo of a Mass Flow controller
  • Can see that flow direction is important
  • Solid-state valves and interface
  • No moving parts=> no wear
  • Needs to be calibrated for each gas
different growth patterns with different flows
Different growth patterns with different flows

 Laminar flow

 Turbulent flow

mechanical obstruction sensors
Mechanical obstruction sensors

Vane flow meter

The faster the fluid flows, the greater the angular displacement.

rotor wheel flow sensor
Rotor wheel flow sensor
  • The rotating vane can be attached to a coil in a magnetic field
  • The current generated in the coil is proportional to the flow rate
pressure drop sensors
Pressure drop sensors

When fluid in a pipe passes through a restriction there is a drop in pressure.

  • Total pressure, Pt, after the constriction is Pt = Ps + Pd
  • Ps is the static pressure,
  • Pd is the dynamic (or impact) pressure
  • Pt is sometimes called the stagnation pressure

How does this work?

bernoulli s equation
Bernoulli’s Equation
  • Where:
  • ρ is the fluid mass density (Ns2m-1)
  • v is the fluid velocity (m/s)
  • g is the acceleration due to gravity
  • z is the height of fluid (often called head)
  • P is the pressure on the fluid
  • This is equivalent to saying that an element of fluid flowing along a streamline trades speed for height or for pressures
  • A consequence is that as flow velocity increases, the pressure on the vessel walls decreases
differential pressure sensors
Differential pressure sensors
  • These sensors change the cross-sectional area A, which increases the velocity v.
  • Since the height of the fluid is constant, the pressure must decrease
  • The amount of material flowing per second does not change, so A1v1=A2v2
  • Bernoulli’s equation becomes ½ ρv12+P1= ½ρv22+P2
  • Combine these expressions to get
differential pressure sensors54
Differential pressure sensors
  • These sensors change the cross-sectional area A, which increases the velocity v
  • Since the height of the fluid is constant, the pressure must decrease after the obstruction
  • The difference in pressures, combined with the cross-sectional area, tells us the velocity before the obstruction
wire mesh flow sensor
Wire mesh flow sensor
  • Used to measure bubble propagation in gases
  • Uses grid of wires to measure electrical conductivity at wire crossing points


images from wire mesh sensor
Images from wire mesh sensor
  • Note the area of laminar flow
  • Light areas are flowing faster


ultrasonic flow sensors
Ultrasonic flow sensors
  • Ultrasonic waves are sound waves above human hearing (>20 kHz)
  • Typical frequencies are 20 kHz - 20 MHz.

Several types of ultrasonic sensors are available- the most common are dynamic or piezoelectric sensors

Remember that sound waves are longitudinal pressure waves caused by vibrations in a medium

  • A typical dynamic sensor is a thin, low mass diaphragm, stretched over passive electromagnet.
  • Such diaphragms operates at frequencies up to 100 kHz
  • Good for Doppler shift intruder alarms (demo)
ultrasonic flow sensors63
Ultrasonic flow sensors
  • Many ultrasonic flow sensors consist of pairs of transducers
  • Each transducer can operate as either a source or a detector of sound waves
dynamic ultrasonic sensors
Dynamic Ultrasonic Sensors
  • As a generator of ultrasonic waves: the drive current creates a magnetic field which pushes against the permanent magnet.
  • As a detector: the motion of the element induces a current in the drive coil
piezoelectric ultrasonic transducers
Piezoelectric ultrasonic transducers
  • We have encountered piezoelectrics in the context of force sensors
  • An extension of this is the use of piezos to convert the compressions and rarefactions of a sound wave into an electrical signal
  • Deforms a crystalline structure under potential stimulation

Used in computers and wrist watches as a time reference.

Operated at resonant frequency (quartz crystal reference)

piezoelectric ultrasonic transducers66
Piezoelectric ultrasonic transducers
  • The piezo transmits when an applied potential distorts crystal
  • Receives when pressure wave distorts crystal
ultrasound baby photos
Ultrasound baby photos

compsoc.dur.ac.uk/ ~ads/ultrasound.jpg

the doppler effect
The Doppler effect

Doppler effect is a shift in frequency from a moving source of waves.

We can use the Doppler effect to measure the velocity of a fluid.


The Doppler effect

One shift upon receiving the signal, the second upon transmitting.

For sound waves reflected off a moving object, there are two shifts:

The net shift is given by:

f is the Doppler shifted frequency

f is the source frequency

v is fluid velocity

 the angle between the ultrasonic beam and the fluid velocity

cs is the speed of sound in the fluid.


Notes on the Doppler Shift

Does not work with pure liquids.

Used as a non-invasive blood flow monitor

Powerful extra tool when combined with ultra-sonic imaging

Doppler shift needs “stuff” to reflect off: either optically active molecules (eg Haemoglobin) or turbulence (bubbles)

doppler blood measurement
Doppler effect can be used to measure variations in blood flow speed

Often used for measuring pulses on animals

Doppler Blood measurement


ultrasonic transit time flowmeter
Ultrasonic transit-time flowmeter

D distance AB between sensors

V is velocity of fluid

Cs speed of sound in fluid

Transit time TAB between A and B depends on the fluid velocity

 angle between transit path and flow

difference in transit times : T=TAB-TBA

The flow velocity is given by: