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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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)
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?
How do we tell when someone is walking down a corridor?
How can we weigh trucks as they pass over a road?
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)
How do we measure an unknown force?
Example: Force on Pendulum, apply force measure deflection.
Apply force to known mass, measure acceleration.
Gravity balance method.
Compare unknown force with action of gravitational force.
Example: Balance scale. (zero-balance 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
Convert the unknown force to a fluid pressure, which is converted using a pressure sensor. Also known as deadweight sensor-used for weight calibrations.
If force is constant, pressure is static or hydrostatic:
If force is varying, pressure is dynamic or hydrodynamic:
Units of Pressure:
There are four basic reference configurations:
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
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.
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 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.
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
MEMs gyroscope based on ‘tuning fork’ design-uses mechanical resonance of micromachined structure to determine orientation.
Images from www.sensorsmag.com/articles/0203/14/
Most common measurement is for blood pressure. More fully:
This is a major application for sensor technology.
The difference in these measurements is the range of measurement; we can often use the same sensor for different measurements
Medical sensors should be:
P=F.R , Where:
This is misleading: in fact, blood vessels change diameter from systemic adjustments and from pulsatile pressure wave.
Four kinds of pressure:
T2 : Peak Pressure (systolic)
Tf: Minimum pressure (diastolic)
Dynamic Average (1/2 peak minus minimum)
Average pressure (arterial)
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.)
=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.
Can achieve pressures up to 80 GPa (or even higher)
So, like, is that big?The diamond Anvil
Pressures are given in Atmospheres
10-31 |- Non equilibrium "pressure" of hydrogen gas in intergalactic space.
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.
10-7 |- 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.
1016 |-Pressure at centre of red-giant star. Pressure at centre of white-dwarf star.
1025 |- Pressure at centre of superdense star.
1028 |- Pressure at centre of neutron star.
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?
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
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)
Cooling of resistive element by fluid flow is measured by Voltmeter
Hot wire anenometer:
Uses two thermometers which supply heat to the gas as well as measuring temperature
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 displacementMechanical obstruction sensors
sensors (a) and (b) turn a constant flow rate into a constant angular velocityRotating mechanical obstruction sensors
When fluid in a pipe passes through a restriction there is a drop in pressure.
How does this work?
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
Used in computers and wrist watches as a time reference.
Operated at resonant frequency (quartz crystal reference)
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.
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.
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)
Often used for measuring pulses on animalsDoppler Blood measurement
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: