2 How do we predict materials failure? Mechanical sensors: motivations.How do we predict materials failure?Strength is the ability to withstand force or stressPredict cracks and collapse in bridges and buildingsAircraft wings (DC-10 metal fatigue: the wings suddenly fell off)Remember stress=force/area
3 How do we measure fluid flow? Usually want laminar flow, not turbulent.Grain silos-want to predict the rate of static buildup to avoid explosions, yet maximize the throughputBeer taps-want to avoid losing the bubblesChemical reactions-want to ensure fluids properly mixed
4 Mechanical Sensors Overview: Definitions Force and pressure sensors Basic pressure sensorsMedical pressure measurement systemsFlow and flow-rate sensors.Mechanical sensors react to stimuli via some mechanical effectThe output may be:Mechanical (e.g. a dial or fluid level)orElectrical (e.g. a voltage or current)
5 Force and Pressure Sensors How do we measure an unknown force?Acceleration MethodExample: Force on Pendulum, apply force measure deflection.Apply force to known mass, measure acceleration.
6 How do we measure hydrostatic pressure in fluids and liquids? 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 liftsHow do divers know how much air they have left in their tanks?
7 How do we tell when someone is walking down a corridor? Pressure sensors:How do we tell when someone is walking down a corridor?How can we weigh trucks as they pass over a road?
8 Force and Pressure Sensors Gravity balance method.Compare unknown force with action of gravitational force.Example: Balance scale. (zero-balance method)
13 Spring MethodUse 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
14 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.
15 Some pressure sensing elements From H. Norton, ‘Sensor and analyzer handbook’Note that these all convert a pressure into an angular or linear displacement. We can then sense the displacement eledctronically or optically.
17 Pressure-sensing method. If force is constant, pressure is static or hydrostatic:Beer in (untapped) kegButane gas bottle.If force is varying, pressure is dynamic or hydrodynamic:Arterial blood pressure.1 Pascal = 1 Newton/m21 atm (Atmospheric pressure) = Pa760 torr = 1 atmUnits of Pressure:
18 Pascal’s PrinciplePressure 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
19 Applications of Pascal’s Principle Disk brakesCar LiftMedical applications
20 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.
21 Can be directly calibrated in Torr Bourdon tube sensorBourdon 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 resistiorMeasure resistance change as the pressure in the active tube is changedCan be directly calibrated in Torr
22 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 readingMembrane sensors can be made very small using micromachining; called microelectromechanical systems (MEMS).We will be discussing MEMS in more detail later.
23 Some MEMS sensors1 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 forcesMEMs gyroscope based on ‘tuning fork’ designImages from
24 Medical pressure measurement. Most common measurement is for blood pressure. More fully:This is a major application for sensor technology.Inter-cardiac blood pressureArterial blood pressureVenous blood pressurePulmonary artery pressureSpinal fluid pressureCentral venous pressureIntraventricular brain pressureThe difference in these measurements is the range of measurement; we can often use the same sensor for different measurements
25 Medical students are often told there is an “Ohm’s law for blood” Medical pressure sensorsminimally invasivesterileelectrically insulatedMedical sensors should be:Medical students are often told there is an “Ohm’s law for blood”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.
26 In fact, the flow rate is better given by Poiseuille’s Law: Where:F is flow in cubic centimetres/secondP is Pressure in dynes per square centimetreη is coefficient of viscosity in dynes/square centimetreR is vessel radius in centimetreL is vessel length in centimetres
27 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)
28 Mean arterial pressure is given by: Blood Pressure AnalysisMean 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 pressureDirect measurement of blood pressure is most accurate but also more dangerous (involves poking tubes into arteries, very invasive.)
29 Open Tube Manometer =density of Manometer fluid Sensing tube tube inserted directly into artery; mercury is poisonous, so need saline bufferMeasure pressure by height of sensing column:Only used in intensive care units.
30 Sphygmomanometry (Korotkoff Method) Inflatable cuff placed on upper arm and inflated until blood can’t flowSound sensor (stethoscope) placed downstreamPressure is releasedWhen can hear blood squirting (Korotkoff sounds), the cuff pressure equals systolic (higher) pressureHear continuous but turbulent flow when cuff pressure equals diastolic pressure.
31 The diamond AnvilOne way to get huge pressures is to use diamonds to squeeze a sampleCan achieve pressures up to 80 GPa (or even higher)So, like, is that big?
32 Relative pressure scale Pressures are given in Atmospheres10-31 |- 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.
33 The Holtz cellThe Holtz cell is a way to achieve huge pressures in a diamond anvilUses a simple lever system to apply pressure
34 The diamond AnvilA photo of a working diamond anvil at the institute for transuranic elements, in Europe
36 Flow and Flow rate.Turbulent flow: chaotic phenomena (whorls, eddies, vortices)Laminar flow: smooth, orderly and regularFlow 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 turbulenceThis begs the question: what makes flow laminar or turbulent?
37 Laminar and Turbulent flow Laminar flow is characterised by :smooth flow linesall fluid velocity in same directionflow velocity is zero at tube wallsflow speed increases closer to tube center
38 Reynolds Number. Reynold’s Number R Where ρ is 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 turbulentR < 2000, flow is laminar
39 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)
40 Cooling of resistive element by fluid flow is measured by Voltmeter Thermal flow SensorCooling of resistive element by fluid flow is measured by VoltmeterHot wire anenometer:
41 Mass Flow controllersUses two thermometers which supply heat to the gas as well as measuring temperatureThe faster that the gas flows, the more heat is removed from the upstream thermometerThe downstream thermometer also measures the heat flow, increasing accuracyNo contact between sensors and gases (no contamination)
42 Photo of a Mass Flow controller Can see that flow direction is importantSolid-state valves and interfaceNo moving parts=> no wearNeeds to be calibrated for each gas
48 Some more mechanical obstruction sensors All these sensors turn a change in flow rate into a change in linear or angular displacement
49 Rotating mechanical obstruction sensors sensors (a) and (b) turn a constant flow rate into a constant angular velocity
50 Rotor wheel flow sensor The rotating vane can be attached to a coil in a magnetic fieldThe current generated in the coil is proportional to the flow rate
51 Pressure drop sensors How does this work? When fluid in a pipe passes through a restriction there is a drop in pressure.Total pressure, Pt, after the constriction is Pt = Ps + PdPs is the static pressure,Pd is the dynamic (or impact) pressurePt is sometimes called the stagnation pressureHow does this work?
52 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 gravityz is the height of fluid (often called head)P is the pressure on the fluidThis is equivalent to saying that an element of fluid flowing along a streamline trades speed for height or for pressuresA consequence is that as flow velocity increases, the pressure on the vessel walls decreases
53 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 decreaseThe amount of material flowing per second does not change, so A1v1=A2v2Bernoulli’s equation becomes ½ ρv12+P1= ½ ρv22+P2Combine these expressions to get
54 Differential pressure sensors These sensors change the cross-sectional area A, which increases the velocity vSince the height of the fluid is constant, the pressure must decrease after the obstructionThe difference in pressures, combined with the cross-sectional area, tells us the velocity before the obstruction
55 Wire mesh flow sensor Used to measure bubble propagation in gases Uses grid of wires to measure electrical conductivity at wire crossing points
62 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 sensorsRemember that sound waves are longitudinal pressure waves caused by vibrations in a mediumA typical dynamic sensor is a thin, low mass diaphragm, stretched over passive electromagnet.Such diaphragms operates at frequencies up to 100 kHzGood for Doppler shift intruder alarms (demo)
63 Ultrasonic flow sensors Many ultrasonic flow sensors consist of pairs of transducersEach transducer can operate as either a source or a detector of sound waves
64 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
65 Piezoelectric ultrasonic transducers We have encountered piezoelectrics in the context of force sensorsAn extension of this is the use of piezos to convert the compressions and rarefactions of a sound wave into an electrical signalDeforms a crystalline structure under potential stimulationUsed in computers and wrist watches as a time reference.Operated at resonant frequency (quartz crystal reference)
66 Piezoelectric ultrasonic transducers The piezo transmits when an applied potential distorts crystalReceives when pressure wave distorts crystal
67 Measuring the speed of sound in a crystal using ultrasound
70 We can use the Doppler effect to measure the velocity of a fluid. 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.
71 The Doppler effectOne 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 frequencyf is the source frequencyv is fluid velocity the angle between the ultrasonic beam and the fluid velocitycs is the speed of sound in the fluid.
72 Notes on the Doppler Shift Does not work with pure liquids.Used as a non-invasive blood flow monitorPowerful extra tool when combined with ultra-sonic imagingDoppler shift needs “stuff” to reflect off: either optically active molecules (eg Haemoglobin) or turbulence (bubbles)
73 Doppler Blood measurement Doppler effect can be used to measure variations in blood flow speedOften used for measuring pulses on animals
74 Ultrasonic transit-time flowmeter D distance AB between sensorsV is velocity of fluidCs speed of sound in fluidTransit time TAB between A and B depends on the fluid velocity angle between transit path and flowdifference in transit times : T=TAB-TBAThe flow velocity is given by: