1. Lecture 7
Demos: U-tube manomoter, Archimedes principle, const fluid height, venturi flowmeter.

2. How do we predict materials failure?
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

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 throughput
Beer taps-want to avoid losing the bubbles
Chemical reactions-want to ensure fluids properly mixed

4. Mechanical Sensors Overview: Definitions Force and pressure sensors
Basic pressure sensors
Medical pressure measurement systems
Flow and flow-rate sensors.
Mechanical sensors react 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)

5. 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.

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 lifts
How 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 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

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.

16. Pressure reference configurations

17. Pressure-sensing method.
If force is constant, pressure is static or hydrostatic:
Beer in (untapped) keg
Butane gas bottle.
If force is varying, pressure is dynamic or hydrodynamic:
Arterial blood pressure.
1 Pascal = 1 Newton/m2
1 atm (Atmospheric pressure) = Pa
760 torr = 1 atm
Units of Pressure:

18. 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

19. Applications of Pascal’s Principle
Disk brakes
Car Lift
Medical 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 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
Measure resistance change as the pressure in the active tube is changed
Can 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 reading
Membrane sensors can be made very small using micromachining; called microelectromechanical systems (MEMS).
We will be discussing MEMS in more detail later.

23. Some 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
Images 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 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

25. Medical students are often told there is an “Ohm’s law for blood”
Medical pressure sensors
minimally invasive
sterile
electrically insulated
Medical 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/second
P is Pressure in dynes per square centimetre
η is coefficient of viscosity in dynes/square centimetre
R is vessel radius in centimetre
L 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 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.)

29. 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.

30. 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 .

31. 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?

32. 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.

33. The Holtz cell
The Holtz cell is a way to achieve huge pressures in a diamond anvil
Uses a simple lever system to apply pressure

34. The diamond Anvil
A photo of a working diamond anvil at the institute for transuranic elements, in Europe

35. Lecture 8

36. 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?

37. 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

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 turbulent
R < 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 Sensor
Cooling of resistive element by fluid flow is measured by Voltmeter
Hot wire anenometer:

41. 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)

42. 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

43. CVD diamond growth reactor

44. Steven’s MFC anecdote

45. Turbulence makes a difference!

46. Different growth patterns with different flows

47. Mechanical obstruction sensors
Vane flow meter

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 field
The 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 + Pd
Ps is the static pressure,
Pd is the dynamic (or impact) pressure
Pt is sometimes called the stagnation pressure
How 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 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

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 decrease
The amount of material flowing per second does not change, so A1v1=A2v2
Bernoulli’s equation becomes ½ ρv12+P1= ½ ρv22+P2
Combine these expressions to get

54. 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

55. Wire mesh flow sensor Used to measure bubble propagation in gases
Uses grid of wires to measure electrical conductivity at wire crossing points

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

61. Cannula pressure-drop sensor

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 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)

63. 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

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 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)

66. Piezoelectric ultrasonic transducers
The piezo transmits when an applied potential distorts crystal
Receives when pressure wave distorts crystal

67. Measuring the speed of sound in a crystal using ultrasound

69. Ultrasound baby photos
compsoc.dur.ac.uk/ ~ads/ultrasound.jpg

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 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.

72. 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)

73. Doppler Blood measurement
Doppler effect can be used to measure variations in blood flow speed
Often used for measuring pulses on animals

74. 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: