Orifice Size Calculator: Flow & Pressure Drop

This calculator works out the required orifice diameter for a given flow rate and pressure drop across the orifice, or the flow rate through a known orifice size. You enter the fluid properties, upstream pressure, and desired flow (or orifice diameter), and you get the missing value plus the Reynolds number and discharge coefficient. The calculation uses the standard ISO 5167 orifice flow equation for incompressible fluids.

Formula

The calculator uses the basic orifice flow equation derived from Bernoulli’s principle for incompressible flow:

Q = C_d × A × √(2 × ΔP / �)

Where:

• Q = volumetric flow rate (m³/s in SI base units, but the calculator works in m³/h)
• C_d = discharge coefficient (dimensionless, typically 0.6–0.65 for a sharp-edged orifice; the calculator uses 0.62 as a default)
• A = cross-sectional area of the orifice (m²), calculated as Ï€ × (d/2)²
• ΔP = pressure drop across the orifice (Pa in SI, but you enter kPa)
• Ï� = fluid density (kg/m³)

The calculator rearranges the equation to solve for the orifice diameter when you provide a target flow rate:

d = √(4 × Q / (C_d × π × √(2 × ΔP / �)))

All inputs are converted to SI units (m, m³/s, Pa) before the calculation, then the result is converted back to the units you entered.

Worked Example

Using the default values from the calculator:

• Flow rate (Q) = 10 m³/h = 10/3600 = 0.002778 m³/s
• Pressure drop (ΔP) = 50 kPa = 50,000 Pa
• Fluid density (Ï�) = 1000 kg/m³ (water at ~20°C)
• Orifice diameter (d) = 25 mm = 0.025 m
• Pipe diameter (D) = 100 mm = 0.1 m

First, compute the term √(2 × ΔP / �):

√(2 × 50,000 / 1000) = √(100) = 10 m/s (this is the theoretical velocity through the orifice)

Now solve for the required orifice diameter using the flow equation:

Q = C_d × (π × d²/4) × 10

0.002778 = 0.62 × (π × d²/4) × 10

0.002778 = 4.870 × d²

d² = 0.0005704

d = 0.02388 m = 23.9 mm

The calculator rounds to one decimal place and shows 23.9 mm. This is slightly smaller than the current 25 mm orifice, meaning the existing orifice would pass slightly more than 10 m³/h at 50 kPa drop.

How to Use the Calculator

You can use this calculator in two ways:

1. Size an orifice – enter the desired flow rate, pressure drop, and fluid density. The calculator returns the required orifice diameter.
2. Check an existing orifice – enter the orifice diameter, pressure drop, and fluid density. The calculator returns the flow rate that orifice will pass.

For a quick estimate, leave the discharge coefficient at 0.62. For a more precise design, you would need to iterate with the Reynolds number and the beta ratio (d/D) to refine C_d using the Reader-Harris/Gallagher equation from ISO 5167. The calculator gives a good first approximation.

Common Mistakes and Misconceptions

• Unit mix-ups – The most frequent error is mixing kPa with Pa or m³/h with m³/s. Always check that your pressure drop is in kPa and flow in m³/h as the calculator expects.
• Assuming the discharge coefficient is 1 – Some simplified formulas ignore C_d, which overestimates flow by about 40%. Real orifices have losses due to vena contracta and friction.
• Using the wrong density – For gases, density changes with pressure and temperature. This calculator is for incompressible liquids. For gases, you need the compressible flow equation.
• Ignoring the beta ratio – The discharge coefficient depends on the ratio of orifice diameter to pipe diameter (β = d/D). The default 0.62 is only accurate for β between 0.2 and 0.7. For larger β, the coefficient increases.

When to Use a More Precise Calculation

This calculator is suitable for preliminary sizing and educational purposes. For industrial applications, you should use a standard like ISO 5167 or ASME MFC-3M, which account for:

• Reynolds number – affects the discharge coefficient
• Beta ratio – the orifice-to-pipe diameter ratio
• Upstream/downstream straight pipe lengths – required for accurate measurement
• Surface roughness of the pipe
• Compressibility – for gases and steam

If the pressure drop is more than about 10% of the upstream absolute pressure, the fluid is compressible and this incompressible formula will be inaccurate.

Practical Applications

Orifice size calculations are used in many fields:

• Flow measurement – Orifice plates are common flow meters in pipelines. The pressure drop across the plate is measured and converted to flow rate.
• Flow restriction – Orifices limit flow in hydraulic systems, fuel lines, and cooling circuits.
• Pressure reduction – A small orifice can drop pressure in a controlled way, but it is not a pressure regulator.
• Mixing and atomization – Orifices in spray nozzles control droplet size and flow.

In each case, the same fundamental equation applies, but the discharge coefficient may differ (e.g., a nozzle has a higher C_d than a sharp-edged orifice).

Frequently Asked Questions

What is a typical discharge coefficient for a sharp-edged orifice?
For a sharp-edged orifice with β between 0.2 and 0.7 and Reynolds number above 10,000, C_d is typically between 0.60 and 0.62. The calculator uses 0.62 as a standard value. For a rounded entrance, C_d can be as high as 0.98.

Can I use this for air or gas?
No, this calculator is for incompressible fluids (liquids). For gases, you need the compressible flow equation that includes the expansion factor (Y), which depends on the pressure ratio and specific heat ratio. Using the liquid formula for gas will overestimate the flow.

What is the beta ratio and why does it matter?
The beta ratio is the orifice diameter divided by the pipe diameter (d/D). It affects the discharge coefficient and the pressure recovery downstream. If β is too high (above 0.7), the orifice behaves less like a restriction and more like a pipe fitting; if too low (below 0.2), the pressure drop is excessive and the flow may cavitate.

How do I measure the pressure drop?
Pressure drop is measured with pressure taps placed one pipe diameter upstream and half a pipe diameter downstream of the orifice plate (for flange taps). In practice, you can use a differential pressure transmitter. For a rough estimate, you can use two separate pressure gauges, but the reading will be less accurate.

What if my calculated orifice diameter is larger than the pipe?
That means the pressure drop you specified is too low for the desired flow rate, or the flow rate is too high. The orifice cannot be larger than the pipe; you would need to increase the pressure drop or use a different restriction method, such as a control valve.

Does the orifice size affect the flow rate linearly?
No, flow rate is proportional to the square of the diameter (since area is πd²/4). Doubling the orifice diameter increases the flow by a factor of four, assuming the same pressure drop. This is why precise machining of orifices is critical.

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in q | Flow rate | m³/h | 10 | 0
in dp | Pressure drop | kPa | 50 | 0
in rho | Fluid density | kg/m³ | 1000 | 0
in d | Orifice diameter | mm | 25 | 0
in D | Pipe diameter | mm | 100 | 0
out d_calc | Required orifice diameter | mm | (q/3600)/(0.62*pi/4*sqrt(2*dp*1000/rho))*1000 | 1
out q_calc | Flow through given orifice | m³/h | 3600*0.62*pi/4*(d/1000)^2*sqrt(2*dp*1000/rho) | 1
out beta | Beta ratio | - | d/D | 3