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Orifice Plate

Q.T.hr 3.9986 Fig,1,2,3 (* D.m² * X * Fa * Δ.Pa sqrt * ρ.kg.m³ sqrt * ≡

π 4 / (3.6 * 2 sqrt * 3.9986

Torricelli v 2 g * h * sqrt ≡

The Stolz formulas replaces all previous methods [AGA, Spink ... All conformities included, the "MassFlow rate" from orifice plate is reliable. The global relative accuracy ± 0.6% or better in the ratio 1 ... 3. Accuracy start degrading around < 0.2 of the nominal design. The function is not linear and reflects from the XTR . 3 types of installation are considered wrt ISO-5167. Fig_1 Flange taps Fig_2 Vena Contracta taps Fig_3 Corner taps

β Fig1 β 2^1 β 4^- (sqrt / 0.5959 0.0312 β 2.1^* + 0.184 β 8^* - 0.002286 β 4^D 1 β 4^- (* / * + 0.000856 β 3^D / * - 0.0029 β 2.5^* R 0.75^/ + (* :

β Fig2 β 2^1 β 4^- (sqrt / 0.5959 0.0312 β 2.1^* + 0.184 β 8^* - 0.09 β 4^1 β 4^- (/ * + 0.01584 β 3^* - 0.0029 β 2.5^* R 0.75^/ + (* :

β Fig3 β 2^1 β 4^- (sqrt / 0.5959 0.0312 β 2.1^* + 0.184 β 8^* - 0.0029 β 2.5^* R 0.75^/ + (* :

R 0.3537 Q D μ * ρ * / * :

Q T/hr ≡ D m ≡ μ cp ≡ ρ kg/m³ ≡ 41 line

Pipe Reynolds e+6
dimensionless R 0.3537 Q D μ * ρ * / * :

Example.1=> Superheated Steam

from Process Engineer Q D μ ρ 14 mat

Operating conditions: 29 bar @ 231.95°C

εo 1.79 105 -^* :

Orifice Plate [316]

εo thermal coefficient of expansion orifice ≡

εT 1.35 105 -^* :

Pipe CS

εT thermal coefficient of expasion pipe ≡

Installation

Flange taps [Fig1]

Orifice Plate data

ms 1 : m/s ≡

P1 2900000 : P1[Pa]Upstream Pressure ≡ Δ 75000 : ΔP[Pa] ... User XTR ≡ Q 100 : MassFlow rate T/hr ≡ t 259 : °C upstream ≡ D 0.3032 : Pipe ID [m] ≡ μ 0.0185 : Viscosity Centipose [cp] ≡ ρ 13.24 : kg/m^3 @ operating conditions ≡ k 1.287 : Isentropic coefficient ≡ 81 sys

Pipe Reynolds e+6 R 0.3537 Q D μ * ρ * / * : 476

Nominal speed [m/s] V 0.3537 Q * ρ D 2^* / : ms 29.1

Gases sizing procedure

βo Sanity check confirmed Fa 1.008987 : X 0.990566 : C0 Q 3.9986 Fa * X * D 2^* Δ ρ * sqrt * / : β 0.5 : β β Fig1 C0 - 0 ≡ β 01 solve : Faβ 12 εo β 4^εT * - (1 β 4^- (/ * t 20 - (* + : Xβ 1 0.41 0.35 β 4^* + (Δ P1 k * / (* - : C Q 3.9986 Faβ * Xβ * D 2^* Δ ρ * sqrt * / : β β Fig1 C - 0 ≡ β 01 solve : 101 line :

1. Initialise Fa=1, X=1 2. re-initialise Fa <= Faβ, X <= Xβ NO change in 'do' => final orifice bore. As long as successive 'do' deviate from ± 0.0001 => re-initialise with last ... ... Fa <= Faβ, X <= Xβ

βo 0.642044

Faβ 12 εo βo 4^εT * - (1 βo 4^- (/ * t 20 - (* + : 1.008987

Xβ 1 0.41 0.35 βo 4^* + (Δ P1 k * / (* - (: 0.990566

do orifice bore diameter mm ≡

mm 1 :

do 1000 βo * D * : mm 194.668

do 1000 βo * D *'mm * : 194.668'mm *

User Notes: 1. Construction Drawing SHALL follow strictly the ISA standard. 2. Fabrication & purchase SHALL be from certified manufacturer. 3. Supplier SHALL be given the dimensionned drawing from Engineer.

Singular losses: Unlike Venturi & Nozzle that profile their flow path from the input/output throat, orifice plate is not a smooth passage, being a drastic restriction to flow. Energy consumption is almost not accountable with Venturi/Nozzle. Differently and from the orifice premise, this metering device consumes some of the pressure head ... how much ? ANSWER below =>

βo Ω 1.005 0.116 βo * - 0.8 βo 2^* - :

Digitised SPink Fig. B-2154 [p.31]

βo Δ ω 0.000101972 Δ * βo Ω * : WC ≡

Nominal head

mH2O 1 :

WC 1 :

βo Ω 0.600746

mH2O 0.0980665 bar * ≡

In English literature WC = Water column

βo Δ ω WC 4.59

Pa 0.000101972 mH2O * ≡

Ω β 0 0.8 0.005 range : i 1 β rows range c i el β i el Ω : for β c augment 31 line :

Singular looses coefficient wrt β

upStream 0.000101972 P1 * : mH2O 295.72

dnStream 0.000101972 P1 * βo Δ ω - : mH2O 291.12

βo Δ ω WC 4.59

Head losses

Sanity check

C βo Fig1 : 0.273143

................ Discharge coefficient

Q 3.9986 βo Fig1 * Faβ * Xβ * D 2^* Δ ρ * sqrt * : 100.0

...MassFlow rate T/hr

S 3.9986 βo Fig1 * Faβ * Xβ * D 2^* ρ sqrt * : 0.3651

S Q Δ sqrt / : 0.3651

..... Reading Control Room Scale Factor

Q S Δ sqrt * : 99.999983

Q.Thr 3.9986 Fig,1,2,3 (* D.m² * X * Fa * Δ.Pa sqrt * ρ.kg.m³ sqrt * ≡

Thr 1 :

plug in empty unit place holder

Q.Thr 3.9986 0.273143 * 0.3032 2^* 0.9906 * 1.009 * 75000 sqrt * 13.24 sqrt * : Thr 100.0

Example.2=> Boiling water

Operating conditions: 29 bar @ 231.95°C

εo 1.79 105 -^* :

Orifice Plate [316]

εo thermal coefficient of expansion orifice ≡

εT 1.35 105 -^* :

Pipe CS

εT thermal coefficient of expasion pipe ≡

Installation

Flange taps [Fig1]

Orifice Plate data

ms 1 : m/s ≡

P1 2900000 : P1[Pa]Upstream Pressure ≡ Δ 25000 : ΔP[Pa] ... User XTR ≡ Q 100 : MassFlow rate T/hr ≡ t 231.95 : °C upstream ≡ D 0.14633 : Pipe ID [m] ≡ μ 0.1145 : Viscosity Centipose [cp] ≡ ρ 824.64 : kg/m^3 @ operating conditions ≡ 71 sys

Pipe Reynolds e+6 R 0.3537 Q D μ * ρ * / * : 3

Nominal speed [m/s] V 0.3537 Q * ρ D 2^* / : ms 2

Liquids sizing procedure

βo Sanity check confirmed Fa 1.00792 : X 1 ... lquid ≡ C0 Q 3.9986 Fa * 1 * D 2^* Δ ρ * sqrt * / : β 0.5 : β β Fig3 C0 - 0 ≡ β 01 solve : Faβ 12 εo β 4^εT * - (1 β 4^- (/ * t 20 - (* + : Xβ 1 ... liquid ≡ C Q 3.9986 Faβ * 1 * D 2^* Δ ρ * sqrt * / : β β Fig3 C - 0 ≡ β 01 solve : 101 line :

βo 0.624002

Faβ 12 εo βo 4^εT * - (1 βo 4^- (/ * t 20 - (* + : 1.007921

do orifice bore diameter mm ≡

mm 1 :

do 1000 βo * D * : mm 91.31

upStream 0.000101972 P1 * : mH2O 295.72

dnStream 0.000101972 P1 * βo Δ ω - : mH2O 294.14

βo Δ ω WC 1.6

Head losses

Fig1_βo Fig2_βo Fig3_βo 31 mat 0.623402 0.618895 0.624002 31 mat ≡

The most commun type of installation is the "Flange Taps" Fig1(β). You can collect each sizing "Fig style" for documentation and vs the supplier calculations.

Note to the Smath Engineer in this document: This document is strictly "Metric System". Not the all world is metric. Let your "non metric user" convert himself in the appropriate "metric" unit system of this Smath document ... Don't do others mistake [?]