Lecture 7
• Demos: U-tube manomoter, Archimedes
principle, const fluid height, venturi
flowmeter.
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 Aircraft wings (DC-10 metal
buildings
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 Grain silos-want to predict the rate
avoid losing the
of static buildup to avoid
bubbles
explosions, yet maximize the
throughput
Chemical reactionswant 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
• Definitions
In this section of
the course, we will
cover:
• Force and pressure sensors
• Basic pressure sensors
• Medical pressure measurement systems
• Flow and flow-rate sensors.
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
How do we measure an unknown force?
Acceleration Method
Apply force to known mass,
measure acceleration.
Example: Force on
Pendulum, apply force
measure deflection.
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.
PF/A
Pressure-sensing method.
If force is constant, pressure
is static or hydrostatic:
• Beer in (untapped) keg
• Butane gas bottle.
• Diving tank
• Arterial blood pressure
If force is varying,
pressure is dynamic or
hydrodynamic:
Units of Pressure:
• Beer flowing in brewery
• Lift in aeroplane wings
• 1 Pascal = 1 Newton/m2
• 1 atm (Atmospheric pressure) = 101325 Pa
• 760 torr = 1 atm
Pressure is usually measured relative to some reference.
There are four basic reference configurations:
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.
http://hyperphysics.phy-astr.gsu.edu/hbase/pasc4.html#c1
Disk brakes
Car Lift
Medical applications
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
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 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
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
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.
This is a major application
for sensor technology.
Most common measurement is
for blood pressure. More fully:
• Arterial blood pressure
• Inter-cardiac blood
pressure
• Venous blood pressure
• Pulmonary artery pressure
• Central venous
pressure
• Spinal fluid 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 pressure sensors
Medical sensors should be:
• minimally invasive
• sterile
• electrically insulated
Medical students are often told there is an “Ohm’s law for blood”
P=F.R ,
Where:
• 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.
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:
Where:
PR
F
8L
4
• 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
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)
http://themodynamics.ucdavis.edu/mustafa/Pulse.htm
Blood Pressure Analysis
t2
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:
1
P
P  dt

t 2  t1 t1
P  P1  ( P2  P1 ) / 3
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
=density of
Manometer fluid
Sensing tube tube
inserted directly
into artery;
mercury is
poisonous, so
need saline buffer
Only used in intensive
care units.
Measure pressure by
height of sensing column:
P  Patm  gh  sgh'
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?
http://ituwebpage.fzk.de/ACTINIDE_RESEARCH/dac.htm
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
pressure
The diamond Anvil
A photo of a
working
diamond anvil
at the institute
for transuranic
elements, in
Europe
Lecture 8
• Demos-Bernoulli’s law.
Flow and Flow rate.
Laminar flow: smooth,
orderly and regular
Mechanical sensors have inertia,
which can integrate out small
variations due to turbulence
Turbulent flow: chaotic
phenomena (whorls,
eddies, vortices)
Flow in a capillary described
by Pouiselle’s law.(But
beware: only valid for laminar
flow)
This begs the question: what makes flow laminar or turbulent?
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.
Reynold’s Number R
Where
V D
R

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
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
Hot wire anenometer:
Cooling of resistive element by
fluid flow is measured by
Voltmeter
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)
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
CVD diamond
growth reactor
Steven’s MFC anecdote
Turbulence makes a
difference!
 Laminar flow
Different
growth
patterns with
different flows
 Turbulent flow
Mechanical obstruction sensors
Vane flow
meter
The faster the fluid flows,
the greater the angular
displacement.
All these
sensors turn a
change in flow
rate into a
change in linear
or angular
displacement
Mechanical obstruction sensors
sensors (a) and
(b) turn a constant
flow rate into a
constant angular
velocity
Rotating mechanical obstruction sensors
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
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
1
2
v  gz  P  constant
2
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
•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
1
2

v  gz  P v1 
2
2
[ Ps  Pt ]
2( P1  P 2)
[( AA12 ) 2  1]
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
• Used to measure bubble
propagation in gases
• Uses grid of wires to
measure electrical
conductivity at wire crossing
points
www.fz-rossendorf.de/FWS/publikat/JB98/jb05.pdf
Images from wire mesh sensor
• Note the area of laminar flow
• Light areas are flowing faster
www.fz-rossendorf.de/FWS/publikat/JB98/jb05.pdf
Cannula pressure-drop sensor
Ultrasonic flow sensors
• Ultrasonic waves are sound waves above human hearing (>20
kHz)
• Typical frequencies are 20 kHz - 20 MHz.
Remember that sound waves
are longitudinal pressure waves
caused by vibrations in a
medium
Several types of ultrasonic
sensors are available- the most
common are dynamic or
piezoelectric sensors
• 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 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
• 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
• 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 transducers
•The piezo
transmits when
an applied
potential distorts
crystal
• Receives when
pressure wave
distorts crystal
Measuring the
speed of sound in a
crystal using
ultrasound
Ultrasound baby photos
compsoc.dur.ac.uk/ ~ads/ultrasound.jpg
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:
2 fv cos( )
f 
cs
The net shift is given by:
f
f
is the Doppler shifted frequency
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
http://www.indusinstruments.com/oldWebsite/Ultrasonic%20Blood%20Flow%20Measurement/dspw_setup.htm
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:
cs2 T
V
2 D cos( )