ME 322: Instrumentation Lecture 15

1. ME 322: InstrumentationLecture 15 February 27, 2012 Professor Miles Greiner

2. Announcements/Reminders • HW 6 due Friday • No lab this week • Career Fair, Thursday, February 27, 2014 • Internships • Prepare for permanent employment next year • www.unr.edu/engineering/careerfair

3. Pipe Speed and Flow Volume Flow Rate • Center line speed increases in the entrance region • In laminar flow (Re <~2000) fully developed flow is parabolic • In Turbulent flow (Re > 104) fully developed profile is flatter

4. Speed and Flow Rate Consistency • Is there a unique centerline speed for every volume flow rate? • What does this relationship dependent on? • Is there a range of centerline speeds in which we expect VC to be for a given volume flow rate?

5. 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 • VC >~ VSlug = Q/A • For fully-developed laminar flow, we expect the velocity profile to be parabolic • where • is the pipe inner radius, and • is the centerline velocity • Relationship between speed and volume flow rate • In HW find that VP = 2VSlug • It’s reasonable to expect (VSlug= Q/A) < VC < (VP = 2VSlug) • In Lab 6 measure Q and VC in a small wind tunnel

6. Lab 6 Air Volume Flow Rate and Centerline Speed in a Wind Tunnel • Plexiglas Tube and Schedule-40 Pipe have different diameters • Control flow rate using a variable speed blower • Cover blower exit for very low speeds • For a range of flow rates, measure • Volume flow Q rate using a Presso Venturi Tube (in pipe) • Centerline speed VC using a Pitot-Static Tube (in Plexiglas tube) • For both measure pressures difference using calibrated transmitters/digital multimeters • Both VC and Q increase with blower flow rate • Is VS < VC < VP?

7. Venturi Tube • Inverted transfer function: • Need , (throat), • This expression needs pipe and throat dimensions • Presso Formulation: • = = • , ): Given by manufacturer • Only need D (pipe) and KPresso

8. In Lab 6 use a Presso Venturi Tube • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2006%20Fluid%20Flow/Lab%20Index.htm • In Lab 6 use 2-inch schedule 40 Pipe, ID = 2.067 inch • PressoData Sheet – Page 10 • Venturi # 38, K = 0.3810 ± 2% (b = 0.6652, but don’t need to this) • Valid for 54,000 < < 137,000 (ReDor Red?)

9. How to find VCand Q (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, PV, and PStat • Air Temperature, T

10. Instrument Schematic Variable Speed Blower Plexiglas Tube Pitot-Static Probe VC Barometer PATM TATM Venturi Tube Q Pipe • 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 – PS • PS = PATM - PG • To measure PP • Use 3-in-WC transmitter • To measure PV • Use 40-in-WC transmitter DTube DPipe PV - Static + 40 in WC Total PP PG Atm IV - - + + 3 in WC 40 in WC IG IP

11. Inlet Pressure and Temperature • Fisher Scientific™ Traceable™ Hand-Held Digital Barometer • Barometric pressure, PATM • Uncertainty: = 5 mbar = 0.5 kPa = 500 Pa (95%?) • (1 mbar = 0.1 kPa = 100 Pa) • Atmospheric Temperature, TATM • = 1°C (95%?) • T[K] = T[°C] + 273.15 • Assume same in tunnel

12. Pressure Transmitter Uncertainty • Pressure • = 998.7 kg/m3, g = 9.82 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

13. 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%)

14. Static Pressure Uncertainty • PStat = PATM – PG (power product?) • Square of absolute uncertainty in result is sum of squares of absolute uncertainty in inputs times coefficient.

15. General Linear Sums

16. Summary • Before Experiment • Use hand held barometer to measure • PATM • TATM • °C

17. During Experiment • For each blower setting find the value and uncertainty of the • Static Pressure, PStat = Work on Board (WOB) • WOB • WOB • Air density WOB • WOB • Centerline speed WOB • WOB • Volume flow rate WOB • WOB

18. Consistency Check • For a given volume flow rate Q • VS = Q/A • VP = 2VS • What area should we use • APipe or ATube ?

19. Measured Results • Determine speed and flow rate uncertainty for a range of blower speeds

21. Lab 6 Air Volume Flow Rate and Centerline Speed in a Wind Tunnel • To measure atmospheric inlet conditions use • Digital Barometer to measure PATM • In Millibar, 1 millibar = 0.1 kPa • wP(atm) = 5 millibar = 0.5 kPa = 500 Pa • Thermometer to measure TATM • T[K] = T[C] + 273.15 • wT = 1 K (68%)

22. Wind Tunnel Schematic Variable Speed Blower Plexiglas Tube Pitot-Static Probe, VC Venturi Tube, Q Pipe DTube DPipe PV - Static + 40 in WC Total PP PG Atm IV - - + + 3 in WC 40 in WC IG IP

23. 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