ME 322: InstrumentationLecture 11

February 11, 2015

Professor Miles Greiner

Pitot probe operation, non-linear transfer function, fluid density, uncertainty, example

Announcement/Reminders• Friday: HW 4 due – Monday: President’s Day Holiday– Wednesday: HW 5 due, Midterm Review– Next Friday: Midterm I

• Thanks for helping at the Science Olympiad. Ms. Davis was very appreciative, and you will receive extra credit.

• Evening with Industry (UNR Society of Women Engineers)– Wednesday, February 25, 2015 (two weeks)– Networking 5:30pm-6:30pm (business attire) – Dinner and Keynote Speaker 6:30-8pm– $25 (or free tickets from ME Office, first come first served)– If you pickup a free ticket, please show-up

• How is Lab 4 going?

Lab 5 Sample Report• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrum

entation/Labs/Lab%2005%20Elastic%20Modulus/Lab%20Index.htm

• Calculate in GPa– Then calculate and – Reference citation • Books: Author, Title, publisher, pages, copyright date

• Make table fonts large enough to see– Include Units

• Write abstract last–Motivation, Methods, Findings, (suggestions)

Fluid Speed

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• Fluid velocity is a vector field– At each location has a magnitude and direction–

• Speed is a scalar – Local velocity Magnitude

– Units:

• Why measure it?–Weather (wind speed), Aircraft air speed, river flow rates,

fan performance, HVAC, confirm CFD simulations

Pressure Method for Measurement

• When an obstruction is placed in a flow it causes the fluid to decelerate and stop, and increases the pressure– PS = Static Pressure

• Measured by an observer traveling with the fluid, or on a flat surface parallel to the flow

– PT = Total (or Stagnation) Pressure • Measured at stagnation point, where V = 0

• Pitot probes are designed to transmit PT

• Pitot-Static probes transmit both PT (inner tube) and PS (outer tube)

V

PSPS

PT > PS PT > PS

Stagnation Point

• Along the blue line, the fluid decelerates and stops (at the Stagnation Point)

• Viscosity does not play an important role in this process• Problem: If the flow changes so the stagnation point is

not at the opening, then the probe will not transmit PT.

V, Speed PS, Static Pressurer, density

V = 0, P = PT

Related Devices

• Boundary Layer probes transmit PT near walls

• Keil probes transmit PT even when flow direction changes

• Aircraft probes measure air speed• Pitot-Static probes are used in Wind Tunnel Labs (6 and 11)

Bernoulli Equation

• Assumptions– Steady, inviscid (no viscosity, m = 0), incompressible

(r = constant), subsonic (V << sound speed)

• – , assume , multiply by r

•

• Transfer Function– Output Reading DP as a function of Measurand V– Measure DP using a pressure transmitter

Reading Measurand

V, PS, r

V = 0, PT

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Ideal (inviscid) Transfer Function

• : Non-linear– Sensitivity increases with – Input resolution is smaller (better) at large than at small

values

• Better for measuring large than for small ones

V

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wDP

wV

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To use Pitot Probe• Invert transfer function:

– The Constant C accounts for viscous effects, which are small• Assume C = 1 unless told otherwise

– Pitot probes generally do not need to be calibrated• Calibration does not change with time (if clean)

– Can be used to calibrate other speed measuring devices• Such as hot-wire or hot-film probes (Lab 11)

Uncertainty in V

• (Power Product?)• Best Estimate• = FIB

How to Find Density• Ideal Gases– (Power Product?)

• P = PS = Static Pressure

• R = Gas Constant = RU/MM

– Ru = Universal Gas Constant = 8.314 kJ/kmol K

– MM = Molar Mass of the flowing Gas– For air: R = 0.2870 kP*m3/kg*K

• T = Absolute Temperature = T[°C] + 273.15• = FIB

• Liquids

– Tables

Water Properties (Appendix B of Text)

British Units

Air (at 1 ATM, not other pressures)

Example• A Pitot-static probe is used to measure air speed

in a wind tunnel. If the air temperature and (static) pressure are T = 27±1°C (95%) and P = 86±2 kPa (95%), and the difference between the total and static pressures is DP = 55±3 Pa (95%), what is the confidence interval for the speed? – Solution (first identify, then do)

• ID: – Fluid, – Do all uncertainties have the same certainty-level?– Likely or Maximum Uncertainty

• Do: on white board

Fluid Flow Rates

• Within a conduit cross section or “area region”– Pipe, open channel, river, blood vessel (not always steady)– V and r can vary over cross section

• Mass Flow Rate, [kg/s, lbm/min, mass/time]– = rAQ (How to measure this for steady liquid flow?)

• Average Density: rA [kg/m3]

• Volume Flow Rate, Q [m3/s, gal/min, cc/hour, Vol/time]– Q = = VAA (How to measure this for steady liquid?)

• Averages– Density: rA =

– Speed: VA [m/s] = =

A

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Many Flow Rate Measurement Devices

• Each relies on different phenomena • When choosing, consider – cost, stability of calibration, imprecision, dynamic response,

flow resistance

Rotameters (variable area)Turbine

Vortex (Lab 11)

Laminar Flow

Coriolis

Variable Area

Pitot-Static Probe • Concentric tubes– Port for inner tube at

stagnation point, measures total (or stagnation) pressure, PT (pressure observed after the flow is stopped)

– Port for outer tube at side, measures static pressure, PS (observed when moving with the flow)

• Use a pressure transmitter to read – DP = PT – PS

• Measurand: U

V, Speed PS, Static Pressurer, density

V = 0 P = PTotal = PT

P = PS

P = PS

P = PT