Lecture 7

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

2. 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. 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

4. 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?

5. Pressure sensors: How do we tell when someone is walking down a corridor? How can we weigh trucks as they pass over a road?

6. Mechanical Sensors • Definitions • Force and pressure sensors • Basic pressure sensors • Medical pressure measurement systems • Flow and flow-rate sensors. 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)

7. 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.

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. Pressure-sensing method. • Beer in (untapped) keg • Butane gas bottle. • Diving tank If force is constant, pressure is static or hydrostatic: • Arterial blood pressure • Beer flowing in brewery • Lift in aeroplane wings If force is varying, pressure is dynamic or hydrodynamic: • 1 Pascal = 1 Newton/m2 • 1 atm (Atmospheric pressure) = 101325 Pa • 760 torr = 1 atm Units of Pressure:

16. Pressure is usually measured relative to some reference. There are four basic reference configurations:

17. 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

18. The bottle bottom breaks when the mouth is struck. Applications of Pascal’s Principle http://hyperphysics.phy-astr.gsu.edu/hbase/pasc4.html#c1 Disk brakes Car Lift Medical applications

19. 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.

20. 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.

21. 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.

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

23. 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/

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 pressure sensors Medical students are often told there is an “Ohm’s law for blood” • 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. 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 • ηis 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) http://themodynamics.ucdavis.edu/mustafa/Pulse.htm

28. 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. 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? The diamond Anvil http://ituwebpage.fzk.de/ACTINIDE_RESEARCH/dac.htm

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

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

35. Demos-Bernoulli’s law. 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 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

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. Thermal flow Sensor Cooling of resistive element by fluid flow is measured by Voltmeter Hot wire anenometer:

41. 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) Mass Flow controllers

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  Laminar flow  Turbulent flow

47. Mechanical obstruction sensors Vane flow meter The faster the fluid flows, the greater the angular displacement.

48. All these sensors turn a change in flow rate into a change in linear or angular displacement Mechanical obstruction sensors

49. sensors (a) and (b) turn a constant flow rate into a constant angular velocity Rotating mechanical obstruction sensors

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