ME 322: Instrumentation
Lecture 11
February 10, 2016
Professor Miles Greiner
Pitot probe operation, non-linear transfer
function, fluid density, uncertainty,
example (units)
Announcement/Reminders
• HW 4 due now (will accept Friday with no penalty)
– Monday: President’s Day Holiday
– Wednesday: HW 5 due, Midterm Review
– Next Friday: Midterm I
• Evening with Industry (UNR Society of Women Engineers)
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Tuesday, February 16, 2015 (Tuesday)
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?
– Sorry about the old sticky glue… 
– We ordered more but they didn’t ship until last Friday
Service-Learning Extra Credit Opportunity
• The Regional Science Olympiad is a competition which
tests middle and high school teams on various science
topics and engineering abilities
• It will be held 8 am to 4 pm Saturday, March 5th 2016
– Where?
• ME 322 students who participate in observing and
judging the events for at least two hours (as reported by
Rebecca Fisher) will earn 1% extra credit.
• To sign up, contact Ms. Fisher, rnfisher@unr.edu, (775)
682-7741 by Wednesday, February 24 to sign up.
– If you sign-up but don’t show-up you will loose 1%!
• Details
– You cannot get extra-credit in two courses for the same
work.
Lab 5 Sample Report
• Calculate 𝐸 in GPa
– Then calculate 𝑤𝐸 /𝐸 and 𝑤𝐸
– Reference citation
• Books: Author, Title, publisher, pages, copyright date
• Make table fonts large enough to see
– Include Units
– Answer questions based on data
• Write abstract last
– Objective, Methods, Findings, (suggestions)
– http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/L
abs/Lab%2005%20Elastic%20Modulus/Lab%20Index.htm
Fluid Speed
• Fluid velocity is a vector 𝑉 𝑥, 𝑦, 𝑧 field
– At each location has a magnitude and direction
– 𝑉 = (𝑢, 𝑣, 𝑤) = (𝑣𝑥 , 𝑣𝑦 , 𝑣𝑧 )
𝑉
• Speed is a scalar
– Local velocity Magnitude
–𝑉=
𝑣𝑥2 + 𝑣𝑦2 + 𝑣𝑧2
– Units:
𝑚 𝑓𝑡 𝑚𝑖𝑙𝑒𝑠
,
,
𝑠 𝑚𝑖𝑛
ℎ𝑟
• Why measure it?
𝑣𝑥
𝑣𝑧
𝑣𝑦
– Weather (wind speed), Aircraft air speed, river flow rates,
fan performance, HVAC, confirm CFD simulations
Pressure Measurement Method
PS
PT > PS
PT > PS PS
V
• 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 (Affects flow!)
• Pitot-Static probes transmit both PT (inner tube) and PS (outer
tube)
Stagnation Point
V Speed
PS Static Pressure
r density
V = 0, P = PT
• 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.
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
V, PS, r
V = 0, PT
• Assumptions
– Steady, inviscid (no viscosity, m = 0), incompressible (r =
constant), subsonic (V << sound speed)
•
2
2 𝑉
𝑉𝑆
2
+
𝑃𝑆
𝜌
𝑉𝑇2
2
+ 𝑧𝑆 𝑔 =
+
𝑃𝑇
𝜌
+ 𝑧𝑇 𝑔
– 𝑉𝑠 = 𝑉, 𝑉𝑇 = 0, assume 𝑧𝑆 = 𝑧𝑇 , multiply by r
• 𝑃𝑇 − 𝑃𝑆 = ∆𝑃 =
1
𝜌𝑉 2
2
Reading
Measurand
• Transfer Function
– Output Reading ∆𝑃 as a function of Measurand 𝑉
– Measure ∆𝑃 using a pressure transmitter, manometer, …
Ideal (inviscid) Transfer Function
∆𝑃 [𝑃𝑎]
𝜕∆𝑃
𝜕𝑉
𝑤∆𝑃
∆𝑃
𝑤𝑉
• ∆𝑃 =
1
𝜌𝑉 2
2
– Sensitivity
𝑉
m
s
V[ ]
: Non-linear
𝜕∆𝑃
𝜕𝑉
= 𝜌𝑉 increases with 𝑉
– Input resolution 𝑤𝑉 = 𝑤∆𝑃 /
than at small values
𝜕∆𝑃
𝜕𝑉
is smaller (better) at large 𝑉
• Better for measuring large 𝑉 than for small ones
To use Pitot Probe
• Invert transfer function: ∆𝑃 =
• 𝑉=𝐶
1
𝜌𝑉 2
2
2∆𝑃
𝜌
– 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-film” probes (Lab 11)
Uncertainty in V
• 𝑉=𝐶
2∆𝑃
𝜌
(Is This a Power Product?)
• Best Estimate
–𝑉=𝐶
•
𝑤𝑉 2
=
𝑉
2∆𝑃
𝜌
Fill in Blank
How to Find Density
• Ideal Gases
–𝜌=
𝑃
𝑅𝑇
=
𝑃 𝑀𝑀
𝑅𝑈 𝑇
(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 [K] = Absolute Temperature = T[°C] + 273.15
•
𝑤𝜌 2
𝜌
= FIB
• Liquids
– 𝜌 = 𝑓𝑛 𝑇 ≠ 𝑓𝑛(𝑃)
– 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:
–
–
–
–
What is the fluid?
Do all uncertainties have the same certainty-level?
Asked for Likely or Maximum Uncertainty?
Units
• Do: on white board
Fluid Flow Rates
A
dA
V, r
𝑚=
𝑑𝑚 =
𝐴
𝜌𝑉𝑑𝐴
𝐴
• 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, 𝑚 [kg/s, lbm/min, mass/time]
– 𝑚 = 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=
𝐴
• Averages
𝑉𝑑𝐴 = VAA (How to measure this for steady liquid?)
– Density: rA = 𝑚/𝑄
– Speed: VA [m/s] = 𝑄/𝐴 = 𝑚/ArA
Many Flow Rate Measurement Devices
Turbine
Rotameters (variable area)
Laminar Flow
Vortex (Lab 11)
Coriolis
• Each relies on different phenomena
• When choosing, consider
Variable Area
– cost, stability of calibration, imprecision, dynamic response,
flow resistance
Pitot-Static Probe
V, Speed
PS, Static Pressure
r, density
P = PS
V=0
P = PTotal = PT
P = PS
P = PT
• 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 = P T – P S
• Measurand: U