ISO 5167 differential flow meter design. Compute Q from ΔP, discharge coefficient Cd, and beta ratio. Real-time Q–ΔP curves and permanent pressure loss comparison.
Meter Type
Parameters
Pipe diameter D₁
mm
Diameter ratio β = D₂/D₁
ISO 5167: 0.2 ≤ β ≤ 0.75
Differential pressure ΔP
kPa
Fluid density ρ
kg/m³
Discharge coefficient Cd
Orifice: ~0.61 / Venturi: ~0.95–0.99
Kinematic viscosity ν
cSt
While paused, move the sliders to update the result instantly.
Results
— m³/h
Flow rate Q
— m/s
Pipe velocity v₁
—
ThroatRe
—
Cd used
— %
Permanent pressure loss rate
—
Rangeability
± —%
Flow uncertainty (95%)
— mm
Throat diameter D₂
Live flow & pressure (continuity + differential pressure)
What exactly is a differential pressure flow meter, and why are there two types (Orifice and Venturi) in this simulator?
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Basically, it's a device that measures flow by creating a pressure drop. You force fluid through a constriction in the pipe. The faster it goes through the narrow part, the more the pressure drops. The two main types are the simple, cheap orifice plate (a thin plate with a hole) and the more complex, efficient Venturi tube (a smooth, tapered constriction). In this simulator, you can switch between them to see how their design affects the flow and pressure.
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Wait, really? So the main difference is just shape? Why does that matter so much? If I slide the "Diameter Ratio (β)" control here, what's actually changing?
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Great question! The shape dictates how the fluid behaves. An orifice plate causes sudden contraction and expansion, creating lots of turbulence and permanent energy loss. A Venturi's smooth contours minimize that. The β ratio (β = D₂/D₁) is the core design parameter. It's the ratio of the throat diameter to the pipe diameter. Try moving that slider: a smaller β (a tighter constriction) gives a larger ΔP for the same flow, which is easier to measure, but it also causes a much larger permanent pressure loss, which costs energy.
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Okay, I see the trade-off. But what's this "Discharge Coefficient (Cd)" parameter? It seems like a magic fudge factor. Why can't it just be 1?
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In practice, it's not magic—it's physics! The ideal flow equation assumes no friction, perfect velocity profiles, etc. Cd is the correction factor that accounts for all real-world effects: friction, turbulence, and the exact geometry. For a well-designed Venturi, it's close to 0.98. For an orifice, it's lower, around 0.6, and it actually changes with flow rate (Reynolds number). That's why in the simulator, you can adjust Cd and see its direct, linear impact on the calculated flow rate Q.
Physical Model & Key Equations
The fundamental equation governing all differential pressure flow meters is derived from the Bernoulli principle and conservation of mass. It relates the measured pressure drop (ΔP) to the volumetric flow rate (Q).
Q = Volumetric flow rate [m³/s] Cd = Discharge coefficient (accounts for real-fluid effects) D2 = Throat (orifice) diameter [m] ΔP = Differential pressure [Pa] ρ = Fluid density [kg/m³] β = Diameter ratio (D₂/D₁)
A critical practical consideration is the permanent pressure loss, which is the irreversible energy cost of using the meter. This is where Orifice and Venturi designs differ drastically.
$$ \text{Orifice Permanent Loss}\approx \Delta P \times \frac{(1-\beta^2)^2}{(1+\beta^2)^2} $$
This equation shows the energy penalty for the simple orifice plate. For a Venturi meter, this loss is typically only 10-20% of the measured ΔP, because most of the pressure is recovered in the diffuser section. The simulator calculates this loss so you can compare the operational cost of each design.
Frequently Asked Questions
Based on ISO 5167, for orifice plates, standard values (e.g., approximately 0.6 for β=0.5) calculated from the beta ratio and Reynolds number are automatically computed. If actual measured values are available, manual input is also possible. An initial value of 0.6 is recommended.
In differential pressure flowmeters, energy is lost due to turbulence and friction when the fluid passes through the constriction, resulting in a pressure loss that does not recover separately from the differential pressure. This loss is large for orifices and small for venturis, so it can be compared on the graph and used for selection.
Please input the actual density in kg/m³ under the operating conditions (temperature and pressure). For ideal gases, it can be calculated from the equation of state. Note that if the effects of compressibility cannot be ignored, the incompressible model in this tool may produce errors.
ISO 5167 recommends a beta ratio in the range of 0.1 to 0.75. In general design, 0.3 to 0.7 is commonly used. If the beta ratio is too small, pressure loss becomes large; if it is too large, the differential pressure becomes small and measurement accuracy decreases, so adjust according to the application.
Real-World Applications
Natural Gas Transmission: Venturi meters are often used at high-pressure pipeline stations because their low permanent pressure loss saves enormous energy costs over hundreds of miles. The accurate measurement is critical for custody transfer—where billions of dollars of gas are bought and sold.
Chemical Process Control: Orifice plates are ubiquitous in chemical plants for monitoring reagent flows. They are cheap, easy to install between flanges, and good enough for many control loops where extreme accuracy isn't required, but reliability is.
Building HVAC Systems: Orifice plates or flow nozzles are installed in the chilled and hot water lines of large buildings to balance the system and ensure each wing gets its designed flow rate, optimizing energy use for heating and cooling.
Automotive Engine Testing: Laminar flow elements (a type of DP meter) are used on engine test stands to measure intake air mass flow with high accuracy. This is essential for calculating engine efficiency and emissions during development.
Common Misconceptions and Points to Note
First, do you think "the larger the differential pressure ΔP, the higher the measurement accuracy"? That's actually a major pitfall. While a small ΔP can indeed make the instrument's resolution an issue, unnecessarily increasing ΔP can cause the diameter ratio β to become too large, increasing the uncertainty of the discharge coefficient Cd, or lead to enormous permanent pressure loss, skyrocketing energy costs. For example, setting ΔP to 1 MPa on a steam line alone can increase boiler fuel costs by millions of yen annually. In practice, a balanced design typically aims to keep ΔP at maximum flow within the range of about 20 to 100 kPa full scale.
Next, the tendency to treat fluid property values (density ρ) as fixed constants. In this simulator too, "density" is an input parameter, but in the actual field, it changes drastically with temperature and pressure. For instance, for the same mass flow of saturated steam, if the pressure drops from 1 MPa to 0.5 MPa, the volumetric flow rate increases by about 1.7 times. This means that without temperature and pressure compensation, the flow rate display will be significantly off. You absolutely need a system that links with temperature and pressure sensors to correct the density in real-time.
Finally, overconfidence that "if it complies with ISO 5167, you'll get the same accuracy everywhere". The standard guarantees accuracy only "when specific installation conditions (straight pipe length, internal pipe roughness, etc.) are met". For example, if there's an elbow or valve immediately upstream of an orifice plate, the flow becomes disturbed, and you won't achieve the Cd specified by the standard. You need at least 10D to 30D (10 to 30 times the pipe diameter) of straight pipe upstream, and in some cases, you should consider installing flow straighteners. Keep in mind that even if the simulator calculates an ideal flow rate, if the field piping layout is "non-ideal", it won't perform as expected.
Enter upstream pipe diameter d₁ (25–600 mm) using the numerical input or slider; typical industrial applications range 50–300 mm for water and steam lines.
Set beta ratio β (d₂/d₁) between 0.4–0.75; lower values increase differential pressure sensitivity but raise permanent loss, while 0.6 is standard for balanced uncertainty in ISO 5167 orifice plates.
Input differential pressure ΔP (5–500 kPa) measured across the meter; select fluid density ρ (kg/m³)—use 1000 for water at 15°C, 0.82 for diesel, or calculate from steam tables.
The calculator outputs flow rate Q (m³/h), discharge coefficient Cd, throat Reynolds number, and permanent pressure loss percentage in real time.
Worked Example
A refinery crude oil line (ρ = 850 kg/m³) uses a 150 mm orifice plate (d₁ = 150 mm, β = 0.65). Measured ΔP = 85 kPa yields: throat diameter D₂ = 97.5 mm, Cd ≈ 0.614 (ISO 5167 sharp-edge), Q = 287 m³/h, upstream velocity v₁ = 4.8 m/s, ThroatRe = 1.2×10⁶, permanent loss ≈ 72%, rangeability 4:1, and flow uncertainty ±2.1% at 95% confidence. Ct factor = 0.973 accounts for thermal expansion of the orifice bore.
Practical Notes
For natural gas (ρ = 0.67–1.2 kg/m³ at line conditions), use compressibility factor Z and enter absolute density; Cd remains ~0.61 but flow scales inversely with density.
Venturi tubes (Cd = 0.98–0.99) recover 80–90% of ΔP as permanent pressure loss, versus 50–70% for orifice plates; select Venturi for cost-critical long-distance pipelines.
ThroatRe below 5000 violates ISO 5167 requirements; increase d₁ or ΔP to stay within 5000–10⁷ range for accuracy.
Install pressure taps 1 pipe diameter upstream and 0.5 d₁ downstream (vena contracta) for ±1.5% repeatability on differential readings.