Use ISO 5167 to Find the Orifice Discharge Coefficient for an Orifice Flow Meter written by: Harlan Bengtson • edited by: Lamar Stonecypher • updated: 9/21/2010 ISO 5167 is a standard for calculating the orifice discharge coefficient of an orifice flow meter, which is widely used for pipe flow rate measurement. The location of the pressure taps for an orifice flow meter was standardized by ISO 5167, allowing better fluid flow measurement.
Introduction ISO 5167, which came out in 1991, set three standard configurations for the pressure taps in an orifice flow meter. It also provided means to calculate the orifice discharge coefficient coefficient for any ratio of orifice diameter diameter to pipe diameter diameter if one of th e standard pressure tap configurations is used. Thus ISO 5167 allows an orifice flow meter to do fluid flow measurement over a wide range of flow rate because the orifice plates in a given orifice flow meter can be changed while still allowing accurate determination of the orifice discharge coefficient.
The orifice meter is the simplest type of differential pressure flow measurement
device. It is just a circular plate (the orifice plate) with a hole in the middle, usually held in place between pipe flanges as shown in the figure at the right. The flow is accelerated due to the constriction, so the pressure is decreased downstream of the orifice plate. The pressure difference, P 1 - P 2, as shown in the figure, can be measured and used to calculate the flow rate passing through the meter from the equation at the right. The equation gives flow rate, Q, in terms of the measured pressure difference, P 1 - P2, the density of the fluid, ρ, the ratio of orifice diameter to pipe diameter, β, the cross-sectional cross -sectional area of the orifice, A o, and the orifice discharge coefficient, C d. For more details about the orifice, flow nozzle, and venturi meter, see the article, " The Orifice, Flow Nozzle, and Venturi Meter for Pipe Flow Measurement."
Pressure Tap Locations
The typical locations of the pressure taps for an orifice flow meter have changed over time. Prior to 1991, the d ownstream pressure tap was typically located at the vena contracta, which is the minimum jet area, downstream from the orifice plate, as shown in the figure in the previous section. The correlations for determination of the orifice discharge coefficient, C d, were based on a vena contracta downstream pressure tap. The downstream distance of the vena contracta from the orifice
plate, however changes with different orifice diameters, so changing orifice size
In 1991 ISO 5167 identified three standard pressure tap configurations for an orifice flow meter. The three configurations are known as corner taps, flange taps, and D - D/2 taps, as illustrated in the figure at the left. The advantage of the ISO 5167 pressure tap configurations is that the distance of the pressure taps from the o rifice plate is given as a fixed distance, or as a function of the pipe diameter, independent of the orifice diameter.
Determination of Orifice Discharge Coefficient ISO 5167 provides an equation (given below) for the orifice discharge coefficient, C d, as a function of β (d/D), Reynolds number (Re), L1 and L2, where L1 is the d istance of the upstream pressure tap from the orifice plate and L 2is the distance of the downstream pressure tap from the orifice plate. As shown in the figure above L 1 = L2 = 0 for corner taps; L1 = L 2 = 1" for flange taps; and L1 = D & L2 = D/2 for D-D/2 taps. The equation for the orifice discharge coefficient is: Cd - 0.5959 + 0.0312 β 2.1 - 0.1840 β 8 + 0.0029 β 2.5(106/Re) 0.75 + 0.0900(L1/D)[β4/(1 - β4)] - 0.0337(L2/D)β3 This equation can be used to find the orifice discharge coefficient for an orifice flow meter with any of the three standard pressure tap configurations, but not for any other arbitrary values of L1 and L2. The introduction of standard pressure tap configurations and the equation for Cd, allows a given orifice flow meter to conveniently use different size orifice openings and cover a wide flow measurement range. Note that an iterative (trial and error) calculation is needed to get a value for C d, because the upstream velocity needed for Re isn't known until C d is known. An Excel spreadsheet works well for the iterative calculation of the orifice discharge coefficient using this equation. For a downloadable Excel template for the use of this equation, see the article, "Excel Templates for Venturi and Orifice Flow Meter Calculations." A U.S Dept. of the Interior reference with information about ISO 5167 for determining the orifice discharge coefficient is provided below.
Images and Reference Images drawn by H. Bengtson REFERENCES for further information: 1. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual
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2. International Organization of Standards - ISO 5167-1:2003 Measurement of fluid flow b y means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Reference number: ISO 5167-1:2003. 3. Bengtson, Harlan H., Flow Measurement in Pipes and Ducts An online continuing education course. ,
ME A S UR E ME NT O F P IP E FL OW R A TE
Measurement of pipe flow rate can use various flow meters, including a differential pressure flowmeter, like the orifice meter, venturi meter and flow nozzle meter. Other types of liquid flow meter are the rotameter , magnetic flow meter, ultrasonic meter, turbine flow meter and coriolis flow meter. 1.
The Orifice, Flow Nozzle, and Venturi Meter for Pipe Flow Measurement
2.
Use ISO 5167 to Find the Orifice Discharge Coefficient for an Orifice Flow Meter Excel Templates for Venturi and Orifice Flow Meter Calculations
3. 4. 5.
Measurement of Pipe Flow Rate with a Rotameter Flow Meter Pipe Flow Measurement with a Magnetic Flow Meter
• 6 years ago This article is mostly about determining the orifice coefficient. See the first and third articles in Harlan Bengtson
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this series for more information about flow rate calculations and choosing the orifice diameter. Those two articles are: "The Orifice, Flow Nozzle, and Venturi Meter for Pipe Flow Measurement," at: http://www.brighthub.com/en..., and "Excel Templates for Venturi and Orifice Flow Meter Calculations,' at:http://www.brighthub.com/en.... o o o o o
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Avinash Kale • 6 years ago
In fire protection systems normally pressure in the charged piping system is 7 Kg/ Cm2 to 10.5 kg / cm2 or higher and when hydrant valve is opened , flow rate of 900 LPM is required but pressure at hydrant valve needs to be restricted to 7 Kg/ Cm2. Hence orifice plates needs to be installed between hydrant valve flange and pipe flange.Which formula needs to be used to decide bore of orifice plate. I would be pleased to receive your advice in this matter - Regards Avinash Kale o o
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sachin kulkarni • 7 years ago
I am working for my academic project on jet formation and flow through nozzle of a hydrogen injector, for an internal combustion engines... I want to know how the coefficient of discharge is calculated for the nozzle, nozzle is constant diameter type, and orifice diameter is 1 mm approximately. o o o o o
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Thomas Müller • 7 years ago
Can I set the Rynolds number of a Critical Venturi Nozzle with only knowing the Pressure in the inflow and outflow and the geometry of the nozzle? o o o o o
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Jiten Patel • 7 years ago
Jagdish, I think you can design the orifice with the standard density at line temp. and pressure. Variation of the density can later be taken care of b y using the pressure and temperature transmitter on the upstream side of the orifice. Then you may multiply the flow rate with Square root of (P*T). This will take care of density variation. So the only change in programming will be flow rate * square of {actual pressure / pressure taken for orifice design) * (temperature orifice is designed for / actual temperature)} . this will take care of density variations o o o o o
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jagdish • 7 years ago
i want to measure the floe rate of the petroleum product in the pipe line whose density is not constant. it is of pressure diffrential type orifice transmitter. how will i find the cofficients and what changes will de done in plc logic. we are using (ab 1756) plc. thank you o o o o
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• 7 years ago Yes, it is correct to calculate the upstream velocity as the volumetric flow rate divided by the pipe cross-sectional area of flow, based on the pipe I.D. Harlan Bengtson
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Jiten Patel • 7 years ago
I have on question I have flow rate, DP, line NB now if I want to design orifice ID requirement.. I need to use following formula Vol. flow rate = Sq. rt .{ 2* Dela P/ (Density* (1- beta^4))} * Gas expansion factor * Gas flow co-efficient * area of orifice bore Form this I can calculate the ID requirement But here in the equation we have to put Cd (gas co -efficinet ) which depends upon the reynolds no. and the reynolds no. depends upon the upstream velocity
my question is how to calculate the upstream velocity Is it the right procedure to devide flow rate with the area w.r.t. pipe ID i.e. Velocity = flowrate (Known)(meter^3/sec)/ area (meter^2) Reynolds no. caculated considering this velocity is perfact or not? o o o o o
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• 7 years ago Determination of the orifice coefficient is an iterative (trial & error) calculation. You can assume a value of Re to get started and adjust that value as needed. See the article, "Excel Templates for Venturi and Orifice Flow Meter Calculations," at http://www.brighthub.com/en..., for an Excel spreadsheet template that can be downloaded to make the iterative calculation of the orifice coefficient. Harlan Bengtson
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Jiten Patel • 7 years ago
Orifice is installed to measure mass flow, volumetric flow, Down stream velocity and upstream velocity The mass or volumetric flow calculation depends upon Gas expansion factor(cd) which relies on reynold no. This reynold no. depends on the velocity Now my question is how does the upstream velocity is calculated from flow rate? if flow rate itself relies on cd, and so reynolds no and so the upstream velocity itself.
function Q = nozzleFlow(d, D, dp, p, T) % nozzleFlow Volumetric flow rate of air through a long radius nozzle. % --- Evaluate fluid properties and other constants % mu = airViscosity(T); % kinematic viscosity mu = 0.015 rho = p/(287*(T+273.15)); % air density from ideal gas law bbeta = d/D; % y = expansionFactor(p,dp,bbeta,1.4); y = 0.9994 area = 0.25*pi*d^2; qcon = area*y*sqrt(2*dp/(rho*(1-bbeta^4))); rcon = rho*d/(area*mu); % --- Initialize and loop until cd converges % tol = 5e-6; it = 0; maxit = 25; cdold = 0; cd = 0.9 ; tol = 5e-6; it = 0; maxit = 250 ; cdold = 0; cd = 0.9 ; while abs(cdold-cd) > tol && it < maxit cdold = cd; Q = cd*qcon; Re = rcon*Q; cd = 0.9986 - 7.006/sqrt(Re) + 134.6/Re; it = it + 1; end if it >= maxit, error('No convergence after %d iterations', it); end
mu = 0.015 rho = p/(287*(T+273.15)); % air density from ideal gas law bbeta = d/D; % y = expansionFactor(p,dp,bbeta,1.4); y = 0.9994 area = 0.25*pi*d^2; qcon = area*y*sqrt(2*dp/(rho*(1-bbeta^4))); rcon = rho*d/(area*mu); % --- Initialize and loop until cd converges % tol = 5e-6; it = 0; maxit = 25; cdold = 0; cd = 0.9 ; tol = 5e-6; it = 0; maxit = 250 ; cdold = 0; cd = 0.9 ; while abs(cdold-cd) > tol && it < maxit cdold = cd; Q = cd*qcon; Re = rcon*Q; cd = 0.9986 - 7.006/sqrt(Re) + 134.6/Re; it = it + 1; end if it >= maxit, error('No convergence after %d iterations', it); end
while ( ppcc > Tolerancia ) x1(i) = A1*Cd ; Re = x1(i) Cd = 0.5961+0.0312*Beta.^2.10.184*Beta.^8+0.0029*Beta.^2.5*(1*10^6/Re).^0.75 ... +0.09*L1*Beta.^4*(1-Beta.^4).^-1-0.0337*L2*Beta.^3 % coeficiente de descarga % if ( Di < 71.2e-3 ) % Cd = Cd+0.011*(0.75-Beta)*(2.8-Di/25.4) % end ppcc = abs((A1 - Re/Cd)/A1) ; Cdi(i) = Cd ; PPCC(i) = ppcc ; i = ( i + 1 ) end x1 ; , Cdi ; , PPCC ; Cdi = Cdi(end) KKK = Cdi/(1-Beta.^4).^0.5 ; % Resultados de caudal Re = A1*Cd ; qm1_ = ( KKK*(pi/4)*Factor_de_expansion*
