XXVI. ASR '00 Seminar, Instruments and Control, Ostrava, April 6-7, 00 Paper 5 Computation of pressure loss for differential producing flowmeters ORLÍKOVÁ, Soňa Ing., Ústav automatizace a měřicí techniky, FEI VUT Brno, Božetěchova, Brno, 6 66 orlikova@dame.fee.vutbr.cz Abstract: The purpose of this paper is to describe the differential producing flowmeters, primarily a mutliport averaging probe. This probe is a special type of the multiport averaging Pitot tube. The pressure loss is one of the most important parameter of the flowmeter. The pressure loss is calculated and compared for the plate, the nozzle, the Venturi tube and MQS probe (a type of multiport averaging probe) in this paper. Keywords: differential producing flowmeter, pressure loss, multiport averaging probe Basic principle of the differential producing flowmeters The fundamental principle for all differentials producing flowmeters is the Bernoulli's streamline energy equation: p V + g z + = const. where V velocity [m.s - ] p pressure density [kg.m -3 ] g*z potential energy [J.kg - ] or p V p V + g z + = + g z + where the subscripts and refer to two points on the same streamline (Figure ). This result of Bernoulli's equation establishes a direct connection between the pressure and velocity. The velocity is greatest where the pressure is least. The flow density is not constant between plates and of Figure for the flow of a gas. Only for very low differential pressure equation () or () will be apply for the gas flow. To correct the equation for the gas expansion, the gas expansion factor is developed from the thermodynamic stead-flow energy equation. When a flow in contracted, either gradually or abruptly, kinetic energy increases at the expense of available potential energy (static pressure). The basic flow equation may be written as a square-root relationship among measured differential pressure section and section in Figure ), density and flow rate Q: Q = k [m 3.s - ] (3) - - () () p (between
The meter constant k includes a discharge coefficient that corrects for contraction characteristics, pressure-tap location, and velocity profile (Reynolds number). For a gas, the density differences caused by gas expansion between measurement taps require an expansion factor correction. v P, vp, z velocity Plate Plate z Datum Figure Bernoulli s equation applied to the differential producer Piping Flanges Flow Primary element Pressure taps Differential pressure Manometer Figure Differential Producing Flowmeter - -
Type of the differential producing flowmeter The differential-producing flowmeters are selected most frequently because of use in many applications. The primary elements are:. Orifice - square edge, quadrant edge, conic edge, integral, eccentric, segmental, etc.. Venturi tube 3. Flow nozzle. Elbow flowmeter 5. Pitot tube 6. Multiport averaging devices (MQS probe or Annubar) These meters are chosen on the basic of the cost, the line size, the fluid being metered, its state (gas, vapour or liquid), the meter range, and the desired accuracy. There is the basic summary of the use of this flowmeters in the Table ([]). Flowmeter Pipe size [mm] Gases (Vapour) Clean Dirty Liquids Clean Viscous Dirty Corrosive Temperature [ C] Pressure [MPa] Accuracy [from URV] Reynolds number Square edged >0 x - x - o o to 50 to ±-% >000 Integral < x - x x - o to 50 to ±-5% >00 Quadratic/ conic >0 - - x x o o to 50 to ±% >00 Eccentric >50 o x o - x o to 50 to ±% >0000 Segmental >00 o x o - x o to 50 to ±% >0000 Venturi tube >50 x o x o o o to 50 to ±-% >75000 Flow nozzle >50 x o x o o o to 50 to ±-% >0000 Pitot tube >75 x - x o - o to 50 to ±5% No limit Elbow flowmeter >50 x o x - o o to 50 to ±.5% >0000 Multiport averaging devices >5 x o x o - o to 50 to ±.5% >0000 X - designed for this application, o - normally applicable, - not designed for this application Table Flowmeter Selection Table 3 Multiport averaging devices The multiport averaging devices are the special type of a pitot tube. The Pitot tube is used for large pipe sizes, when the fluid is a clean liquid or gas. Like the Pitot tube the multiport averaging devices must be used for clean liquid or gas. Ease of installation, low cost, very low pressure lost and good performance make these devices competitive with other - 3 -
differential producers in many industrial applications. There are several designs available - cylinder probe (e.g. MQS probe made by VAVRA s.r.o), diamond-shapes probe (e.g. Annubar made by Dietrich Standard Corp.), etc. The MQS probe [3] is the multiport averaging device made by VAVRA s.r.o. The differential pressure p for MQS probe is equal: p = () p c p ú where p c total pressure p ú static pressure Figure 3 Multiport averaging probe The average pipe velocity v may be written as v = k [m.s - ] (5) Then the volumetric flow rate is Q v = S v = S k [m 3.s - ] (6) where S pipe area [m ] k probe coefficient [-] density [kg.m -3 ] Pressure loss Except for obstructionless flowmeters (magnetic and ultrasonic) every flowmeter has a permanent pressure loss. The pressure loss is a difference of static pressures that are measured between two points. The first point is in front of the flowmeter, where the effect of the dynamic pressure is negligible. The second point is behind the flowmeter, where the refresh of the static pressure by expanse is complete. - -
The permanent pressure loss ω is calculated using the pressure loss coefficient by K v ω = (7). Pressure loss for differential producing flowmeters The equal for the pressure loss is different for the different type of the differential producing flowmeters. There are the equals for the plates, the nozzles, the Venturi tubes and for MQS probe (type of the multiport averaging probe) in the Table 3. Flowmeter Pressure loss Flow coefficient [-] Orifice plate Nozzle Venturi tube MQS probe ω = ω = C ω = ω = K v C + C C + C + C C C = 0,5959 + 0,03 0,8 Table Equation for the differential producing flowmeter. Example I have calculated the pressure loss for the plate (D = 00 mm, d = 50 mm), the nozzle (D = 00 mm, d = 50 mm), the Venturi tube (D = 00 mm, d = 50 mm) and for MQS probe ( D = 00 mm, k = 0,765). The average pipeline velocity was from 5 to 5 m.s - and Re < 00000. The calculating pressure losses for differential producing flowmeters listen above are in the Table 3. Figure shows pressure loss for this flowmeters dependent on the average pipeline velocity. 8 + 0,009 C = 0,99 0,6,,5, 6 0 Re,5 ( 0,0075 0,0033 ) For 00mm D 800 mm 0,3 0,75 C = 0,98 K =, S S 0 S S 0 3 0,75 6 0 Re,5 5 Conclusion The differential producing flowmeters are the most widely used in industrial process measurement and control applications. The pressure loss is one of their parameter that has influence to the using. The pressure loss is high for the plates, the nozzles and the Venturi tubes (Figure 3). The multiport averaging probes have a low pressure loss. This is one of their positives. - 5 -
v [m.s - ] Basic parameter MQS Probe Orifice plate Nozzle Venturi tube Q m [m 3.s - ] Re [-] Κ [] C [-] C [-] 5 0,039 3733 3,6,07 6,5 0,608 33,03 0,985 63,69 68, 6 0,07 776 60,0,07 3,68 0,608 66,5 0,983 38,0 387, 7 0,055 539 873,03,07 3, 0,607 636,0 0,98 59,89 58,03 8 0,063 5970,97,07, 0,607 83,65 0,98 680,33 690,69 9 0,07 676 7,0,07 53,9 0,606 055,6 0,98 86,35 875,9 0 0,079 767 788,8,07 65,79 0,606 30,7 0,980 065,95 08,53 0,086 8090 65,7,07 79,6 0,606 579,66 0,980 9,3 309,7 0,09 8955 578,88,07 9,7 0,606 88,5 0,979 537,89 559,76 3 0,0 9705 308,3,07,9 0,605 09,6 0,979 806,3 83,66 0,0 078 35,,07 8,95 0,605 56, 0,979 096,6 5, 5 0,8 90 035,93,07 8,03 0,605 95, 0,979 07,68,0 6 0,6 903 593,90,07 68, 0,605 335,6 0,979 70,78 778,9 7 0,33 6866 588,00,07 90,3 0,605 3786, 0,978 3095,8 337,8 8 0, 338 588,5,07 3,6 0,605 6,6 0,978 37,77 359,0 9 0,9 79 68,65,07 37,50 0,605 733, 0,978 3869,65 39,06 0 0,57 95 787,0,07 63,6 0,605 56,7 0,978 89,3 36,98 0,65 5676 795,90,07 90, 0,605 5785,7 0,978 730,0 793,76 0,73 679 8700,75,07 38,3 0,60 635,57 0,978 59,87 56,0 3 0,8 76 95,76,07 38,03 0,60 693,85 0,978 5677,3 575,9 0,88 790 0358,9,07 378,95 0,60 756,5 0,978 683,00 665,30 5 0,96 86567,3,07,9 0,60 807,65 0,978 670,5 6799,55 Table 3 Pressure loss for differential producing devices Pressure loss for differential producing devices 9000 8000 7000 pressure loss 6000 5000 000 3000 000 000 MQS probe Orrifice plate Nozzle Venturi tube 0 5 0 5 0 5 velocity [m.s - ] Figure Graph of the pressure loss - 6 -
6 References [] MILLER, R. W. Flow Measurement Engineering Handbook. New York: McGraw-Hill Publishing Company, 989. 083 pp. ISBN 0-07-006-7. [] SABERSKY, R. H., ACOSTA, A. J., HAUPTMANN, E. G. Fluid Flow. New York: Macmillan Publishing Company, 989. 537 pp. ISBN 0-0-96850-7. [3] MQS probe. Data sheets, Brno: firma VAVRA s.r.o, 998. [] ČSN ISO 567- Měření průtoku tekutin pomocí snímačů diferenčního tlaku, část. Praha: Federální úřad pro normalizaci a měření, 993. 68 s. [5] PARKER, S. P. Fluid Mechanics Source Book. New York: McGraw-Hill Publishing Company, 987. 7 pp. ISBN 0-07-0550-3. - 7 -