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Title: Physics:%20Principles%20and%20Applications

Lecture 7
New section Mechanical Sensors
  • 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
Mechanical (e.g. a dial or fluid level) or
Electrical (e.g. a voltage or current)
The output may be
Force and Pressure Sensors
How do we measure an unknown force?
Acceleration Method
Example Force on Pendulum, apply force measure
Apply force to known mass, measure acceleration.
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 Fkx ,
k 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.
Some pressure sensing elements
Note that they all convert a pressure into an
angular or linear displacement
  • From H. Norton, Sensor and analyzer handbook

  • Pressure reference configurations

Pressure-sensing method.
If force is constant, pressure is static or
  • Beer in (untapped) keg
  • Butane gas bottle.

If force is varying, pressure is dynamic or
  • Arterial blood pressure.
  • 1 Pascal 1 Newton/m2
  • 1 atm (Atmospheric pressure) 101325 Pa
  • 760 torr 1 atm

Units of Pressure
Pascals 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 Pascals Principle
Disk brakes
Car Lift
Notes on Pascals principle
Pascals principle is always true in hydrostatic
But, 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 hydodynamic systems where flow is
non-turbulent and the pipe orifice is small
compared with its length.
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
Membrane pressure sensors
Subdivided into bellows, thin plate and diaphragm
All 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).
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
Medical pressure measurement.
Most common measurement is for blood pressure.
More fully
This is a major application for sensor
  • Inter-cardiac blood pressure
  • Arterial blood pressure
  • Pulmonary artery pressure
  • Venous blood 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
Ohms law for blood
Medical pressure sensors
  • 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.

PF.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
Poiseuilles Law
  • F is flow in cubic centimetres/second
  • P is Pressure in dynes per square centimetre
  • ? is coefficient of viscosity in dynes/square
  • 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)

Mean arterial pressure is given by
Blood Pressure Analysis
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
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
Measure pressure by height of sensing column
Only used in intensive care units.
Sphygmomanometry (Korotkoff Method)
  • Inflatable cuff placed on upper arm and inflated
    until blood cant 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
  • So, like, is that big?

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
Flow and Flow rate.
Turbulent flow chaotic phenomena (whorls,
eddies, vortices)
Laminar flow smooth, orderly and regular
Flow in a capillary described by Pouiselles
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 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 R
? 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 gt 4000, flow is turbulent R lt 2000, flow
is laminar
Flow Sensors
Many sensors measure flow rate.
Mass flow rate mass transferred per unit time
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
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

Photo of a Mass Flow controller
  • Can see that flow direction is important
  • Solid-state valves and interface
  • No moving partsgt no wear
  • Needs to be calibrated for each gas

CVD diamond growth reactor
Stevens MFC anecdote
Turbulence makes a difference!
Different growth patterns with different flows
Mechanical obstruction sensors
Vane flow meter
Some more mechanical obstruction sensors
All these sensors turn a change in flow rate into
a change in linear or angular displacement
Rotating mechanical obstruction sensors
sensors (a) and (b) turn a constant flow rate
into a constant angular velocity
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?
Bernoullis Equation
  • Where
  • ? 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

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 A1v1A2v2
  • Bernoullis equation becomes ½ ?v12P1 ½
  • Combine these expressions to get

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
Images from wire mesh sensor
  • Note the area of laminar flow
  • Light areas are flowing faster
Cannula pressure-drop sensor
Ultrasonic flow sensors
  • Ultrasonic waves are sound waves above human
    hearing (gt20 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 sensors
  • Many ultrasonic flow sensors consist of pairs of
  • 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

Used in computers and wrist watches as a time
Operated at resonant frequency (quartz crystal
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
(No Transcript)
Ultrasound baby photos 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
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

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 ?TTAB-TBA
The flow velocity is given by