In a flow metering device based on the Bernoulli Equation the downstream pressure aft an obstruction will equal lower than the upstream pressure sensation in front. To understand orifice, nozzle and venturi meters it is necessity to explore the James Bernoull Equation.
The Bernoulli Equation
Assuming a horizontal fall (neglecting the minor elevation difference between the measurement points) the Bernoulli Equation can be qualified to:
p1 + 1/2 ρ v1 2 = p2 + 1/2 ρ v2 2 (1)
where
p = pressure (Pa, psf (lb/ft2))
ρ = density (kg/m3, slugs/ft3)
v = feed velocity (m/s, ft/s)
The equivalence can be adapted to vertical run by adding elevation heights:
p1 + 1/2 ρ v1 2 + γ h1 = p2 + 1/2 ρ v2 2 + γ h2 (1b)
where
γ = specialised weight of runny (kg/m3, slugs/ft3)
h = elevation (m, ft)
Assuming uniform velocity profiles in the upriver and downriver flow - the Continuity Equality can be expressed every bit
q = v1 A1 = v2 A2 (2)
where
q = rate of flow (m3/s, ft3/s)
A = flow area (m2, foot2)
Combining (1) and (2), assumptive A2 < A1, gives the "ideal" equation:
q = A2 [ 2(p1 - p2) / ρ(1 - (A2 / A1)2) ]1/2 (3)
For a minded geometry (A), the flow rate arse be determined by measurement the pressure difference p1 - p2.
The theoretical flow rate q leave in practice Be smaller (2 - 40%) due to nonrepresentational conditions.
The ideal equation (3) sack comprise modified with a discharge coefficient:
q = c d A2 [ 2 (p1 - p2) / ρ (1 - (A2 / A1)2) ]1/2 (3b)
where
cd = discharge coefficient
The discharge coefficient cd is a function of the honey oil size - OR orifice opening - the
arena ratio = Avc / A2
where
Avc = area in "vena contracta" (m2, ft2)
"Vein Contracta" is the nominal jet orbit that appears scarce downriver of the restriction. The viscous effect is usually expressed in price of the not-dimensional parameter Reynolds Number - Re.
Ascribable the Benoulli and the Persistence Equating the velocity of the fluid bequeath embody at it's highest and the blackmail at the lowest in "Vena Contracta". After the metering device the speed bequeath decrease to the same point as before the obstruction. The pressure recover to a force per unit area lower than the pressure before the obstruction and adds a psyche expiration to the flow.
Equation (3) can be qualified with diameters to:
q = cd (π / 4) D2 2 [ 2 (p1 - p2) / ρ (1 - d4) ]1/2 (4)
where
D2 = opening, Robert Charles Venturi or honker inside diameter (m, ft)
D1 = upstream and downstream tabor pipe diameter (m, ft)
d = D2 / D1 diameter ratio
π = 3.14...
Equation (4) can be modified to mass flow for fluids by simply multiplying with the density:
m = cd (π / 4) D2 2 ρ [ 2 (p1 - p2) / ρ (1 - d4) ]1/2 (5)
where
m = mass menses (kg/s)
When measuring the mass menses in gases, its obligatory to kind the pressure reduction and change in density of the fluid. The formula above can exist used with limitations for applications with comparatively small changes in pressure and tightness.
The Porta Plate
The porta meter consists of a flat orifice plate with a circular hole drilled in it. Thither is a blackmail tap upstream from the orifice home base and another good downstream. There are in general three methods for placing the lights-out. The coefficient of a meter depends connected the position of the lights-out.
- Flange location - Pressure tap location 1 inch upstream and 1 inch downstream from face of opening
- "Vena Contracta" location - Pressure tap positioning 1 pipe diameter (actual inside) upstream and 0.3 to 0.8 pipework diam downstream from face of orifice
- Pipe location - Pressure tap location 2.5 times nominal pipe diameter upstream and 8 multiplication nominal tobacco pipe diameter downriver from face of orifice
The expelling coefficient - cd - varies considerably with changes in area ratio and the Reynolds number. A discharge coefficient cd = 0.60 may be interpreted American Samoa standard, but the value varies observably at down in the mouth values of the Reynolds bi.
| Release Coefficient - cd | ||||
|---|---|---|---|---|
| Diameter Ratio d = D2 / D 1 | Reynolds Phone number - Re | |||
| 104 | 105 | 106 | 107 | |
| 0.2 | 0.60 | 0.595 | 0.594 | 0.594 |
| 0.4 | 0.61 | 0.603 | 0.598 | 0.598 |
| 0.5 | 0.62 | 0.608 | 0.603 | 0.603 |
| 0.6 | 0.63 | 0.61 | 0.608 | 0.608 |
| 0.7 | 0.64 | 0.614 | 0.609 | 0.609 |
The pressure recovery is limited for an porta crustal plate and the permanent insistence loss depends primarily on the area ratio. For an area ratio of 0.5 the head loss is about 70 - 75% of the orifice differential.
- The orifice meter is recommended for clean and dirty liquids and some slurry services.
- The rangeability is 4 to 1
- The pressure loss is medium
- Typical accuracy is 2 to 4% of to the full shell
- The required upstream diameter is 10 to 30
- The viscousness effect is high
- The congener be is low
Example - Orifice Course
An orifice with diameter D2 = 50 mm is inserted in a 4" Sch 40 steel tabor pipe with inside diameter D1 = 102 mm. The diam ratio can be calculated to
d = (50 mm) / (102 millimeter)
= 0.49
From the shelve to a higher place the discharge coefficient can be estimated to some 0.6 for a wide range of the Reynolds number.
If the smooth is water with density 1000 kilogram/m3 and the pressure difference over the orifice is 20 kPa (20000 Protactinium, N/m2) - the mass flow done the shrill can be calculated from (5) as
m = 0.6 (π / 4) (0.05 m)2 (1000 kilo/m3) [ 2 (20000 Pa) / (1000 kilogram/m3) (1 - 0.494) ]1/2
= 7.7 kg/s
Orifice Figurer
The orifice calculator is settled on eq. 5 and can live put-upon to calculate mass flow through an orifice.
cd - empty coefficient
D2 - orifice diam (m)
D1 - pipe diameter (m)
p1 - upriver coerce (Pa)
p2 - downstream pressure (Pa)
ρ - density of fluid (kg/m3)
Typical Orifice Kv Values
| Orifice Size (mm) | Kv (m3/h) |
|---|---|
| 0.8 | 0.02 |
| 1.2 | 0.05 |
| 1.6 | 0.08 |
| 2.4 | 0.17 |
| 3.2 | 0.26 |
| 3.6 | 0.31 |
| 4.8 | 0.45 |
| 6.4 | 0.60 |
| 8 | 1.5 |
| 9 | 1.7 |
| 13 | 3 |
| 16 | 4 |
| 18 | 4.5 |
| 19 | 6.5 |
| 25 | 11 |
| 32 | 15 |
| 38 | 22 |
| 51 | 41 |
| 64 | 51 |
| 76 | 86 |
| 80 | 99 |
| 100 | 150 |
| 125 | 264 |
| 150 | 383 |
References
- American Society of Mechanically skillful Engineers (ASME). 2001. Measurement of fluid run over using small bore precision orifice meters. ASME MFC-14M-2001.
- Supranational Organisation of Standards (ISO 5167-1:2003). Measurement of unstable feed by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-division conduits running full. Reference number: ISO 5167-1:2003.
- International Organization of Standards (ISO 5167-1) Amendment 1. 1998. Measurement of fluid flow past means of pressure differential devices, Split up 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Credit total: ISO 5167-1:1991/Amd.1:1998(E).
- Ground Society of Mechanical Engineers (ASME). B16.36 - 1996 - Orifice Flanges
The Venturi Meter
In the venturi meter the fluid is accelerated through and through a converging cone of angle 15-20o and the pressure deviation between the upstream go with of the retinal cone and the pharynx is measured and provides a signal for the range of flow.
The disposable slows down in a cone with smaller angle (5 - 7o ) where most of the kinetic energy is born-again back to pressure zip. Because of the cone and the step-by-step reduction in the domain there is no "Venous blood vessel Contracta". The flow area is at a minimum at the throat.
High pressure and energy recovery makes the venturi meter suitable where only elfin pressure heads are available.
A discharge coefficient cd = 0.975 butt make up indicated as orthodox, but the value varies noticeably at low values of the Reynolds number.
The imperativeness recovery is very much amended for the venturi meter than for the orifice plate.
- The venturi tube is suitable for clean, dirty and viscous unfrozen and some slurry services.
- The rangeability is 4 to 1
- Pressure loss is low-toned
- Typical accuracy is 1% of rumbling range
- Required upstream pipe duration 5 to 20 diameters
- Viscosity effect is high
- Relative cost is medium
References
- International Establishment of Standards - ISO 5167-1:2003 Measuring of fluid flow by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in disk-shaped cross-sectional conduits running brimful. Reference count: ISO 5167-1:2003.
- American Society of Mechanical Engineers ASME FED 01-Jan-1971. Fluid Meters Their Possibility And Application- One-sixth Variation
The Nozzle
Nozzles used for decisive fluid's flowrate done pipes can be in trine different types:
- The ISA 1932 nozzle - developed in 1932 by the International Organization for Normalisation or ISO. The ISA 1932 nozzle is common outside USA.
- The long radius nozzle is a variant of the ISA 1932 nozzle.
- The Venturi schnozzle is a interbred having a convergent section similar to the ISA 1932 nozzle and a divergent section similar to a venturi metro flowmeter.
| Discharge Coefficient - cd | ||||
|---|---|---|---|---|
| Diameter Ratio d = D2 / D 1 | Reynolds Number - Atomic number 75 | |||
| 104 | 105 | 106 | 107 | |
| 0.2 | 0.968 | 0.988 | 0.994 | 0.995 |
| 0.4 | 0.957 | 0.984 | 0.993 | 0.995 |
| 0.6 | 0.95 | 0.981 | 0.992 | 0.995 |
| 0.8 | 0.94 | 0.978 | 0.991 | 0.995 |
- The flux nozzle is recommended for both clean and dirty liquids
- The rangeability is 4 to 1
- The relative pressure going is medium
- Typical accuracy is 1-2% of full range
- Compulsory upstream pipe distance is 10 to 30 diameters
- The viscosity effect high
- The congenator toll is medium
References
- American Guild of Machinelike Engineers ASME FED 01-Jan-1971. Fluid Meters Their Theory And Application- Sixth Edition
- International Organization of Standards - ISO 5167-1:2003 Measurement of fluid flow by way of pressure differential devices, Part 1: Porta plates, nozzles, and Venturi tubes inserted in circular cross-division conduits running full. Reference number: ISO 5167-1:2003.
Example - Kerosene Flowing Through a Venturi Meter
The pressure difference DP = p1 - p2 between upstream and downstream is 100 kPa (1 105 N/m2). The taxonomic category gravity of kerosine is 0.82.
Upriver diam is 0.1 m and downstream diameter is 0.06 m.
Density of kerosene can be calculated arsenic:
ρ = 0.82 (1000 kilogram/m3)
= 820 (kg/m3)
- Density, Precise Weight and Proper Gravitational force - An introduction and definition of density, specific slant and specialised gravity. Formulas with examples.
Upriver and downriver area can be calculated A:
A1 = π ((0.1 m)/2)2
= 0.00785 (m2)
A2 = π ((0.06 m)/2)2
= 0.002826 (m2)
Theoretical flow can be calculated from (3):
q = A2 [ 2(p1 - p2) / ρ(1 - (A2/A1)2) ]1/2
q = (0.002826 m2) [2 (105 N/m2) / (820 kg/m3)(1 - ( (0.002826 m2) / (0.00785 m2) )2)]1/2
= 0.047 (m3/s)
For a pressure difference of 1 kPa (0,01x105 N/m2) - the theoretical fall rear be calculated:
q = (0.002826 m2) [2 (0.01 105 N/m2) / (820 kg/m3)(1 - ( (0.002826 m2) / (0.00785 m2) )2)]1/2
= 0.0047 (m3/s)
The mass flow can be calculated as:
m = q ρ
= (0.0047 m3/s) (820 kg/m3)
= 3.85 (kg/s)
Flow and Alter in Pressure Dispute
Annotation! - The rate of flow varies with the square root of the pressure difference.
From the example above:
- a tenfold increase in the flow rate pace requires a one hundredfold step-up in the pressure difference!
Transmitters and Control System
The nonlinear relationship have impact on the imperativeness transmitters operating range and requires that the electronic pressure transmitters have the capability to linearizing the signal before transmitting it to the control system.
Truth
Due to the not linearity the scorn rate is limited. The truth strongly increases in the lower region of the operating range.
- More approximately Flow rate Meters as Orifices, Venturi meters, and Nozzles
- Hydraulics
- The Johann Bernoulli Equation
- The Continuity Equation
- TurnDown Ratio and Flow Measurement Devices - An introduction to Crook Down Ratio and hang measure accuracy.
If the Velocity Across the Entire 45.7 - Cm Diameter Disc of the Fan
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