ME 322: Instrumentation Lecture 6
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ME 322: Instrumentation Lecture 15 February 22, 2016 Professor 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 ππΆ 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 ππΆ to be? Possible Centerline Speeds • At the pipe entrance and for fully-developed turbulent flow, the velocity profile is relatively flat compared to fullydeveloped laminar flow – ππΆ β³ ππππ’π = π/π΄ • For fully-developed laminar flow, we expect the velocity profile to be parabolic – π ππ = π02 −π 2 , π02 where • π0 is the pipe inner radius, and • ππ is the centerline velocity (for a parabolic profile). – Relationship between speed and volume flow rate • π= π΄ πππ΄ = π0 ππ 0 π02 π02 − π 2 2ππππ • In HW show that ππ = 2ππππ’π • It’s reasonable to expect (ππππ’π = π/π΄) < ππΆ < (ππ = 2ππππ’π ) • In Lab 6 measure π and ππΆ 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 π rate using a Presso Venturi Tube (in pipe) – Centerline speed ππΆ using a Pitot-Static Tube (in Plexiglas tube) • For both measure pressures difference using calibrated transmitters/digital multimeters • Both ππΆ and π increase with blower flow rate – Check to see if ππππ’π < ππΆ < ππ Venturi Tube • Inverted transfer function: π = π π· πΆπ΄2 1−π½4 2βπ π π 4 – Need π½ = , π΄2 = π 2 (throat), πΆ = π π ππ· = – These are all characteristics of the venture tube. 4ππ ,π½ ππ·π = π π· • But πΆ = π π ππ· is based on knowing d and D. • Presso Formulation: – π= π΄2 π΄1 π΄1 – πΎPresso = πΆ 1−π½ 4 πΆπ· π½ 2 1−π½ 4 2βπ π = π΄1 πΆπ½2 1−π½4 2βπ π = π 2 π· 4 πΎPresso = ππ π ππ· : Given by manufacturer – Only need D (pipe) and KPresso (not ~1, but don’t need π½ or π΄2 ) 2βπ π 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/L abs/Lab%2006%20Fluid%20Flow/Lab%20Index.htm • πΎπ = 0.3810 ± 2% (b = 0.6652, but don’t need to this) • Valid for 54,000 < π π < 137,000 (ReD or Red?) • π= π 4 2 π·ππππ πΎπ – Easier to use than π = 2βπ π πΆπ΄2 1−π½4 2βπ π π = πΆ 4 π2 1−π½4 2βπ π How to find ππ and π (and uncertainties)? • Pitot-Static Probe – ππ = πΆ 2ππ πAir (power product?) • Presso Venturi Tube –π= π 4 2 π·ππππ πΎππππ π π 2ππ£ ππ΄ππ (power product?) • Both need air-density – ππ΄ππ = πππ‘ππ‘ π π΄ππ π (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 Variable Speed Blower Pipe Venturi Tube Q Plexiglas Tube Pitot-Static Probe VC DTube DPipe 40 in WC - PV + IV Static Total + 3 in WC • To measure PATM and TATM Barometer PATM TATM PP IP - PG + Atm IG 40 in WC – 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 • To measure PV (Volume) (IP) – Use 40-in-WC transmitter (IV) Inlet Pressure and Temperature • Fisher Scientific™ Traceable™ Hand-Held Digital Barometer • Barometric pressure, PATM – Uncertainty: π€ππ΄ππ = 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: π€π = 1°C (assume 95%?) – T[K] = T[°C] + 273.15 – Assume tunnel and atmospheric temperatures are the same Pressure Transmitter Uncertainty • Pressure – π = ππ πβ = ππ π(πΉπ) πΌ−4 ππ΄ 16 ππ΄ • ππ = 998.7 kg/m3, g = 9.81 m/s2 • FS = (3 or 40 inch) 2.54 ππ 1 π 1 πππβ 100 ππ = 0.0762 ππ 1.016 π • Manufacturer stated uncertainty: 0.25% Full Scale – (95%?) – For FS = 3 inch WC • PFS = rWghFS = 2.54 ππ (998.7 kg/m3)(9.81 m/s2) (3 inch) 1 πππβ • wP = 0.0025 PFS = 1.9 Pa 1π 100 ππ = 746.6 Pa – For FS = 40 inch WC • PFS = rWghFS = kg/m3)(9.81 m/s2) (998.7 (40 • wP = 0.0025 PFS = 25 Pa 2.54 ππ 1 π inch) 1 πππβ 100 ππ = 9954 Pa Static Pressure • PStat = PATM – PG – Use for ππ΄ππ = πππ‘ππ‘ π π΄ππ π , RAir = 0.2870 kPa-m3/kg-K – Want kPa • Inputs – PATM • Measure using barometer • π€ππ΄ππ = 500 Pa = 0.5 kPa (95%) – PGAGE • Measure using 40 inch WC gage • π€ππΊπ΄πΊπΈ = 25 Pa = 0.025 kPa (95%) Static Pressure Uncertainty • PStat = PATM – PG (power product?) – Need to use general formula for likely uncertainty: – π€πππ‘ππ‘ 2 = = 2 πΏπππ‘ππ‘ 2 π€π π=1 πΏπ₯π 2 πΏπππ‘ππ‘ π€ππ΄ππ + πΏππ΄ππ 2 = 1π€ππ΄ππ + 2 = 1 0.5kPa πΏπππ‘ππ‘ π€ππΊ πΏππΊ −1π€ππΊ 2 2 + −1 0.025kPa 2 • ππππ‘ππ‘ = 0.5006 πππ • Square of absolute uncertainty in result is sum of squares of absolute uncertainty in inputs times coefficient. General Expression Likely Error of “Linear Sums” • π = ππ + ππ + ππ + β― + = • π€π 2 = 2 ππ π€π πππ • π€π 2 = ππ€π 2 + • π€π 2 = ππ π€π 2 ππ ππ 2 2 ππ ππ = π€π + π€π ππ ππ 2 ππ π€π + β― ππ ππ€π 2 + ππ€π 2 + β― + Summary Variable Speed Blower Pipe Venturi Tube Q Pitot-Static Probe VC DTube DPipe 40 in WC Plexiglas Tube - PV + IV Static Total + 3 in WC • Before Experiment • Use hand held barometer to measure – PATM • πππ΄ππ = 0.5 πππ – TATM • πππ΄ππ = 1°C Barometer PATM TATM PP IP - PG + Atm IG 40 in WC During Experiment • For each blower setting find the value and uncertainty of the – Static Pressure, PStat = PATM – Pgage (Power product, linear sum, other?) 2 • ππππ‘ππ‘ = Work on Board – Air density ππ΄ππ = • πππ΄ππ 2 ππ΄ππ πππ‘ππ‘ π π΄ππ ππ΄ππ = Work on Board – Centerline speed ππ = πΆ • π ππ 2 ππ • π 2ππ πAir (Power product, linear sum, other?) = Work on Board – Volume flow rate π = ππ 2 (Power product, linear sum, other?) π 4 = Work on Board 2 π·ππππ πΎππππ π π 2ππ£ ππ΄ππ (PP, LS, other?) Consistency Check • For eac volume flow rate π (show calculations next time) – ππππ’π = π/π΄ – ππ = 2ππππ’π • 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 • 2 ππππ‘ππ‘ 2 = 1πππ΄ππ + −1πππΊ 2 = 1 0.5kPa 2 + −1 0.025kPa • ππππ‘ππ‘ = 0.5006 πππ – Air density ππ΄ππ = • πππ΄ππ 2 ππ΄ππ = 1 πππ‘ππ‘ π π΄ππ ππ΄ππ ππππ‘ππ‘ 2 πππ‘ππ‘ – Centerline speed ππ = πΆ • πππ 2 ππ = ππΆ 2 1 πΆ + – Volume flow rate π = • ππ 2 π = 2 ππ·ππππ 2 π·ππππ + −1 ππ΄ππ 2ππ πAir 1 π ππ 2 ππ π 4 πππ΄ππ 2 2 1 ππ − 2 π π΄ππ π΄ππ + 2 π·ππππ πΎππππ π π + 1 ππΎππππ π π 2 πΎππππ π π + 2 2ππ£ ππ΄ππ 1 π ππ£ 2 2 ππ£ + 1 ππ − 2 π π΄ππ π΄ππ 2 2 Wind Tunnel Schematic Variable Speed Blower Pipe Plexiglas Tube Venturi Tube, Q DTube DPipe 40 in WC Pitot-Static Probe, VC - PV + IV Static Total + 3 in WC PP IP - PG + Atm IG 40 in WC
