ME 322: InstrumentationLecture 15

February 22, 2016Professor Miles Greiner

Relating speed and flowrate, Lab 6 equipment, Presso flow coefficient, linear sum uncertainty

Announcements/Reminders

• HW 6 due Friday• Lab today (Lab 5) but not the rest of this week

Regional Science Olympiad• Tests middle and high school teams on various science

topics and engineering abilities• Will be held 8 am to 4 pm Saturday, March 5th 2016

– On campus: SEM, PE and DMS• ME 322 students who participate in observing and judging

the events for at least two hours (as reported) will earn 1% extra credit.

• To sign up, contact Rebecca Fisher, rnfisher@unr.edu, (775) 682-7741 – by Wednesday, February 24

• Details– You cannot get extra-credit in two courses for the same work. – If you sign-up but don’t show-up you will loose 1%!

Pipe Speed and Volume Flow Rate

• Centerline speed increases in the entrance region– Even though mass (and volume) flow rate is constant

• In fully-developed flow, speed profile V(r) is– Parabolic in laminar flow (Re <~2000), and develops slowly– Flatter in Turbulent flow (Re > 104), and develops rapidly

Speed and Flow Rate Consistency

• Does the centerline speed increase with flow rate? Yes or No?

• Is there a unique centerline speed for every volume flow rate and every location? Yes or No?

• What does this “relationship” dependent on?• For a given volume flow rate, what is the range

of centerline speeds in which we expect to be?

Possible Centerline Speeds• At the pipe entrance and for fully-developed turbulent flow,

the velocity profile is relatively flat compared to fully-developed laminar flow–

• For fully-developed laminar flow, we expect the velocity profile to be parabolic– where

• is the pipe inner radius, and • is the centerline velocity (for a parabolic profile).

– Relationship between speed and volume flow rate

• In HW show that

• It’s reasonable to expect () < < ()• In Lab 6 measure and in a small wind tunnel

Lab 6 Air Volume Flow Rate and Centerline Speed in a Wind Tunnel

• Plexiglas Tube and Schedule-40 Pipe have different diameters• We control flow rate using a variable-speed blower

– Also cover blower exit for very low speeds• For a range of flow rates, measure

– Volume flow rate using a Presso Venturi Tube (in pipe) – Centerline speed using a Pitot-Static Tube (in Plexiglas tube)

• For both measure pressures difference using calibrated transmitters/digital multimeters

• Both and increase with blower flow rate– Check to see if < <

Venturi Tube

• Inverted transfer function: – Need , (throat), – These are all characteristics of the venture tube.

• But is based on knowing d and D.

• Presso Formulation: – = = – : Given by manufacturer – Only need D (pipe) and KPresso (not ~1, but don’t need )

In Lab 6 use a Presso Venturi Tube

• In Lab 6 use 2-inch schedule 40 Pipe, ID = 2.067 inch– Presso Data Sheet – Page 10, Venturi # 38

• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2006%20Fluid%20Flow/Lab%20Index.htm

• = 0.3810 ± 2% (b = 0.6652, but don’t need to this)• Valid for 54,000 < < 137,000 (ReD or Red?)

• – Easier to use than

How to find and (and uncertainties)?• Pitot-Static Probe– (power product?)

• Presso Venturi Tube– (power product?)

• Both need air-density– (power product?) • RAir = 0.2870 kPa-m3/kg-K

• Need to measure– Pressure differences PP (pitot), PV (volume), and PStat – Air Temperature, T

Instrument Schematic

• To measure PATM and TATM – Use hand-held digital-barometer

• Is PStat <, = or > than PATM?– Use 40-in-WC transmitter to find Gage Pressure PG = PATM – PStat (IG)– PStat = PATM - PG

• To measure PP (Pitot)– Use 3-in-WC transmitter (IP)

• To measure PV (Volume)– Use 40-in-WC transmitter (IV)

DTubeDPipe

PP PG

PV Static

Total+ +--IV

IP IG

+-

Variable SpeedBlower Pipe

PlexiglasTube

Pitot-Static Probe VC

Venturi TubeQ

Atm40 in WC

3 in WC 40 in WC

BarometerPATM TATM

Inlet Pressure and Temperature

• Fisher Scientific™ Traceable™ Hand-Held Digital Barometer• Barometric pressure, PATM

– Uncertainty: = 5 mbar = 0.5 kPa = 500 Pa (assume 95%?)• Units: 1 bar = 105 Pa; so 1 mbar = 100 Pa = 0.1 kPa

• Atmospheric Temperature, TATM

– Assume: = 1°C (assume 95%?)– T[K] = T[°C] + 273.15– Assume tunnel and atmospheric temperatures are the same

Pressure Transmitter Uncertainty• Pressure

• = 998.7 kg/m3, g = 9.81 m/s2

• FS = (3 or 40 inch)

• Manufacturer stated uncertainty: 0.25% Full Scale– (68%?)– For FS = 3 inch WC

• PFS = rWghFS = (998.7 kg/m3)(9.81 m/s2) (3 inch) = 746.6 Pa• wP = 0.0025 PFS = 1.9 Pa

– For FS = 40 inch WC• PFS = rWghFS = (998.7 kg/m3)(9.81 m/s2) (40 inch) = 9954 Pa• wP = 0.0025 PFS = 25 Pa

Static Pressure• PStat = PATM – PG – Use for , RAir = 0.2870 kPa-m3/kg-K–Want kPa

• Inputs– PATM • Measure using barometer• = 500 Pa = 0.5 kPa (68%)

– PGAGE • Measure using 40 inch WC gage• = 25 Pa = 0.025 kPa (68%)

Static Pressure Uncertainty

• PStat = PATM – PG (power product?) – Need to use general formula for likely uncertainty:

• Square of absolute uncertainty in result is sum of squares of absolute uncertainty in inputs times coefficient.

General Expression Likely Error of “Linear Sums”

Summary

• Before Experiment• Use hand held barometer to measure– PATM

– TATM • °C

DTubeDPipe

PP PG

PV Static

Total+ +--IV

IP IG

+-

Variable SpeedBlower Pipe

PlexiglasTube

Pitot-Static Probe VC

Venturi TubeQ

Atm40 in WC

3 in WC 40 in WC

BarometerPATM TATM

During Experiment• For each blower setting find the value and

uncertainty of the– Static Pressure, PStat = PATM – Pgage (Power product, linear

sum, other?) • Work on Board

– Air density (Power product, linear sum, other?)

– Centerline speed (Power product, linear sum, other?)

– Volume flow rate (PP, LS, other?)

Consistency Check

• For eac volume flow rate (show calculations next time)– –

• What area should we use– APipe or ATube ?

During Experiment• For each blower setting find the value and

uncertainty of the – Static Pressure, PStat = PATM – Pgage

– Air density

– Centerline speed

– Volume flow rate

Wind Tunnel Schematic

DTubeDPipe

PP PG

PV Static

Total+ +--IV

IP IG

+-

Variable SpeedBlower Pipe

PlexiglasTube

Pitot-StaticProbe, VC

VenturiTube, Q

Atm40 in WC

3 in WC 40 in WC