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Fluid Mechanics

Venturi Meter Simulator

Design a Venturi meter, which gently contracts a pipe to create a pressure drop and measures the volumetric flow from that drop. Adjust the upstream and throat diameters and the differential pressure to see the flow rate, velocity, Reynolds number and permanent pressure loss update in real time.

Parameters
Upstream pipe diameter D₁
mm
Inner diameter of the straight pipe ahead of the Venturi
Throat diameter D₂
mm
Inner diameter of the narrowest contraction (throat). Keep it below D₁
Differential pressure Δp (upstream − throat)
kPa
Pressure difference measured between the two tappings
Fluid density ρ
kg/m³
About 998 for water at 20°C; differs for oils and brines
Discharge coefficient Cd
Ratio of actual to ideal flow. A Venturi runs at 0.95-0.99
Fluid viscosity μ
mPa·s
Used for the Reynolds number; about 1.0 for water at 20°C
Results
—
Volumetric flow Q (m³/h)
—
Throat velocity V₂ (m/s)
—
Upstream velocity V₁ (m/s)
—
Beta ratio β (=D₂/D₁)
—
Reynolds number (throat)
—
Permanent pressure loss (kPa)
—
Venturi tube — flow and pressure profile

Fluid passes through a converging cone, the throat and a long, gentle diffuser. Velocity rises and pressure drops at the throat, then most of the pressure recovers along the diffuser. The lower curve is the pressure distribution along the axis.

Flow vs differential pressure Δp
Flow vs beta ratio β
Theory & Key Formulas

$$Q=C_d\,A_2\sqrt{\dfrac{2\,\Delta p}{\rho\,(1-\beta^4)}},\qquad \beta=\frac{D_2}{D_1}$$

Volumetric flow Q. Cd: discharge coefficient, A₂: throat area, Δp: differential pressure, ρ: fluid density, β: beta ratio. Because flow scales with √Δp, the meter is least accurate at low flow rates.

$$A_1=\frac{\pi D_1^2}{4},\qquad A_2=\frac{\pi D_2^2}{4},\qquad V_2=\frac{Q}{A_2},\quad V_1=\frac{Q}{A_1}$$

Upstream area A₁ and throat area A₂, with the velocity at each section. From continuity Q=A·V, a narrower throat means a faster velocity.

$$Re=\frac{\rho\,V_2\,D_2}{\mu},\qquad \Delta p_{\text{loss}}=(0.10+0.05\,\beta)\,\Delta p$$

Throat Reynolds number Re and permanent pressure loss. μ: fluid viscosity. Because the diffuser recovers pressure, the permanent loss is only about 10-15% of the differential pressure.

What is the Venturi Meter Simulator?

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A "Venturi meter" is that pipe with a pinched waist in the middle, right? How can a simple narrowing tell you the flow rate?
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Exactly — that waist is the star. The key is Bernoulli's equation. When the pipe narrows, the same amount of fluid has to squeeze through, so the flow speeds up. And when the flow speeds up, the pressure falls by exactly that much. So the pressure at the narrow throat is lower than in the wide upstream pipe. Measure that pressure difference (the differential pressure Δp) and you can run Bernoulli's equation backwards to get the flow rate. Move the Δp slider on the left — the flow Q tracks it.
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I see! But when I double Δp, the flow does not double. It takes about a four-fold Δp to double the flow. Why is that?
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Good catch. Flow is proportional to the square root of the differential pressure — Q ∝ √Δp. So Δp has to rise four-fold for the flow to double. Look at the "Flow vs differential pressure" chart: it rises steeply near the origin and then flattens out, the classic square-root curve. This property has a weakness: at low flow the differential pressure becomes very small, so measurement accuracy drops. That is why a Venturi meter is at its best when there is a decent flow running.
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If you just want a pressure difference, a plate with a sharp hole would do it too. Why bother with a smooth, gradual waist?
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That sharp-holed plate is exactly the "orifice plate". Yes, it produces a differential pressure too. But the decisive difference is "pressure recovery". A Venturi tube has a long, gentle diverging cone (the diffuser) after the throat. The flow decelerates slowly there, so it never "separates" from the wall, and most of the pressure lost at the throat comes back. The result: only 10-15% of the differential pressure is lost permanently. An orifice plate, with its sharp edge, makes the flow separate abruptly, and 50-80% of the differential pressure vanishes as permanent loss. That difference shows up directly on the pump's electricity bill.
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There is a "beta ratio β" on the left. What is it, and how does it matter in design?
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β is the throat diameter D₂ divided by the upstream pipe diameter D₁, β=D₂/D₁ — the single most important design parameter of a Venturi tube. Make β small (a narrow throat) and you get a larger differential pressure at the same flow, easier to measure, because the (1−β⁴) term shrinks. But velocity rises and so does the pressure loss. Make β large and the loss drops, but the differential pressure shrinks and accuracy suffers. Sweep the throat diameter on the "Flow vs beta ratio" chart and you will see that tug-of-war. In practice β is chosen around 0.4-0.75, balancing the required differential pressure against the loss you can tolerate.
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The discharge coefficient Cd sits at 0.98, very close to 1. What does that value mean?
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Cd is the ratio of "the flow the ideal Bernoulli equation predicts" to "the actual flow". In reality, viscosity builds a boundary layer near the wall and the flow is not perfectly uniform, so the real flow is a little less than theory. That is why Cd is slightly below 1. A Venturi tube has such smooth flow that Cd is 0.95-0.99 — very close to 1, which is exactly why it is called "high accuracy". For comparison, an orifice plate has a Cd of about 0.6, a far bigger correction. Keep in mind that Cd depends slightly on the Reynolds number too, so it drops in the low-flow region.

Frequently Asked Questions

From Bernoulli's equation and continuity, the volumetric flow rate is Q = Cd·A₂·√(2Δp / (ρ(1−β⁴))), where A₂ is the throat area, Δp is the pressure drop between the upstream pipe and the throat, ρ is the fluid density, β=D₂/D₁ is the beta ratio and Cd is the discharge coefficient. Because flow is proportional to the square root of the differential pressure, a four-fold rise in Δp only doubles the flow. This tool computes Q with this formula and also reports it in m³/h.
Both are differential-pressure flow meters that contract the pipe to create a pressure drop, but their permanent pressure loss differs greatly. A Venturi tube decelerates the flow through a long, gentle diverging cone and recovers most of the pressure without separation, so its permanent loss is only about 10-15% of the differential pressure. A sharp-edged orifice plate is cheaper but causes the flow to separate abruptly, losing 50-80% of the differential pressure permanently. Choose a Venturi for accuracy and energy efficiency, an orifice for low cost.
The beta ratio β=D₂/D₁ is the most important design parameter of a Venturi tube. A smaller β (a narrower throat) produces a larger differential pressure at the same flow, making it easier to measure, but raises the velocity and pressure loss. A larger β reduces the loss but produces a smaller differential pressure and lower measurement accuracy. In practice β is chosen between 0.4 and 0.75, balancing the required differential-pressure range against the allowable pressure loss. Standards such as ISO 5167 also cover this range.
The discharge coefficient Cd is the ratio of the actual flow rate to the flow predicted by the ideal Bernoulli equation. In reality, viscous boundary layers and non-uniform flow make the actual flow slightly lower than theory, so Cd < 1. A Venturi tube has very smooth flow, so Cd is 0.95-0.99 — close to 1, which is why it is so accurate. An orifice plate has a Cd of about 0.6, requiring a much larger correction. Cd also depends on the Reynolds number and drops at low flow rates, so care is needed there.

Real-World Applications

Water-supply and treatment plants: Water-treatment works and distribution pumping stations measure the flow through large-bore mains with Venturi tubes. On a transmission line running 24 hours a day, any pressure loss the flow meter itself creates feeds straight back into pumping power, so a low-loss Venturi is preferred. Even with a higher up-front cost than an orifice plate, the long-term electricity savings often pay it back.

Boiler feedwater in thermal and nuclear plants: Feedwater flow into a boiler is one of the most critical measurements for plant efficiency and safety, and a high-accuracy Venturi tube (classical Venturi or Venturi nozzle) is used. Because the flow is smooth and Cd is stable, the meter is highly repeatable and gives a reliable flow value based on standards such as ISO 5167.

HVAC ducts and industrial processes: Differential-pressure flow meters are also widely used to manage gas and liquid flows in air-conditioning ducts and process piping. Compressible gases need a density correction, but an incompressible estimate like this tool is still useful for first-pass sizing as long as the Mach number is low. In chemical plants, lined Venturi tubes are sometimes chosen for corrosive fluids.

Devices that exploit the Venturi effect: Beyond flow measurement, the pressure drop at the throat — the "Venturi effect" — is applied widely: fuel pickup in a carburettor, suction in ejectors and aspirators, and dust collection in a Venturi scrubber. Visualizing the "pressure drops at the throat" behaviour in this tool helps you understand the principle behind all of those devices with the same logic.

Common Misconceptions and Pitfalls

The most common pitfall is assuming the differential pressure Δp equals the permanent pressure loss. The differential pressure Δp measured at the tappings is only the "instantaneous" pressure difference between the upstream pipe and the throat. The pressure dropped at the throat is largely recovered in the diffuser that follows. What is finally lost permanently is only about 10-15% of the differential pressure for a Venturi tube. A large differential pressure does not mean you are throwing away that much energy. An orifice plate, by contrast, recovers almost nothing, and 50-80% of its differential pressure becomes permanent loss. Keep "Δp = a signal for measurement" and "permanent loss = the energy actually lost" as separate things.

Next, assuming the discharge coefficient Cd is a fixed constant. This tool treats Cd as a constant set by a slider, but in reality Cd depends on the Reynolds number. In particular, at low flow or high viscosity where the Reynolds number is small, the boundary layer becomes relatively thick and Cd drops. Standards (ISO 5167) define a lower Reynolds-number limit below which Cd can be treated as constant; below that, a Venturi tube's accuracy is not guaranteed. Always check this point for viscous oils or applications where the flow rate varies widely.

Finally, assuming a narrower throat always makes a better flow meter. It is true that a smaller beta ratio β produces a larger Δp and makes measurement easier. But as the throat velocity rises, not only does the pressure loss grow — in a liquid, the throat pressure can fall below the saturated vapour pressure and vapour bubbles form and collapse, a phenomenon called cavitation. Cavitation disturbs the reading and erodes the pipe wall. β should be chosen by looking at three things together: ease of measurement, the allowable pressure loss, and the cavitation margin (the throat pressure staying safely above the vapour pressure).

How to Use

  1. Enter upstream pipe diameter D₁ (mm) and throat diameter D₂ (mm) to define the contraction ratio
  2. Input the measured pressure drop ΔP (kPa) across the venturi section using a differential manometer or transducer
  3. Select fluid density ρ (kg/m³): water=1000, oil=860, air at sea level=1.225
  4. Click Calculate to obtain volumetric flow Q using the ISO 5167 discharge coefficient equation

Worked Example

Steel pipeline carrying water with D₁=100 mm, D₂=60 mm (β=0.6), measured ΔP=15 kPa, ρ=1000 kg/m³. Simulator yields: Q=42.8 m³/h, V₁=1.51 m/s, V₂=4.19 m/s, throat Reynolds number=251,400, permanent loss=2.1 kPa. Beta ratio of 0.6 is typical for industrial applications balancing sensitivity and permanent head loss.

Practical Notes

  1. Maintain throat Reynolds number above 100,000 to ensure coefficient accuracy; below 50,000 accuracy degrades significantly
  2. For high-viscosity oils (ρ=860 kg/m³), pressure drop increases nonlinearly—recalibrate manometer range if ΔP exceeds 50 kPa
  3. Beta ratios 0.4–0.75 minimize permanent pressure loss while maintaining measurement precision; ratios below 0.3 cause unacceptable irreversible head loss
  4. Classical venturi with C-form recovery section recovers 80–90% of differential pressure; nozzle types recover only 30–50%