Fluid Mechanics

Orifice Flow Calculator

Simplified sharp-edged liquid-orifice calculator for flow rate, required orifice diameter, pressure drop, driving head, or discharge coefficient using a user-supplied Cd value.

Formula Q = C_d A sqrt(2 Delta p / rho); Q = C_d A sqrt(2 g h) (simplified liquid model)Reviewed Sep 9, 2026

Orifice flow is commonly estimated from a simplified discharge relationship in which actual liquid flow equals the ideal Bernoulli-based flow multiplied by a discharge coefficient, C_d. This calculator uses that sharp-edged incompressible-liquid model so you can solve for flow rate, required orifice diameter, pressure drop, driving head, or discharge coefficient from a known operating point. It is intentionally a simplified tool: you provide C_d directly, and the page does not attempt a full ISO 5167 orifice-meter correlation.

Calculation Bench

Calculation Basis

Solve for

01Orifice Diameter

d · Effective diameter of the sharp-edged round opening.

02Fluid Density

rho · Liquid density used to relate pressure drop to ideal discharge velocity.

03Pressure Drop Across Orifice

Delta p · Differential pressure drop across the orifice itself, not upstream pressure alone.

04Discharge Coefficient

C_d · Empirical coefficient entered as a decimal between 0 and 1. This page does not estimate C_d automatically, and the result is highly sensitive to this value.

This page uses a simplified sharp-edged liquid-orifice model with user-entered discharge coefficient. Use differential pressure across the opening itself, and do not treat the result as a certified ISO-orifice-meter calculation. If a back-calculated discharge coefficient exceeds 1, recheck the inputs and the suitability of this model.

Solution

Enter the required values to calculate flow rate.

Q = C_d A √(2 Delta p / rho)

Formula Sheet

Q = C_d A \sqrt{\dfrac{2\Delta p}{\rho}}

d = \sqrt{\dfrac{4Q}{\pi C_d \sqrt{2\Delta p/\rho}}}

\Delta p = \dfrac{\rho}{2}\left(\dfrac{Q}{C_d A}\right)^2

C_d = \dfrac{Q}{A\sqrt{2\Delta p/\rho}}

Q = C_d A \sqrt{2gh}

d = \sqrt{\dfrac{4Q}{\pi C_d \sqrt{2gh}}}

h = \dfrac{\left(Q/(C_d A)\right)^2}{2g}

C_d = \dfrac{Q}{A\sqrt{2gh}}

QFlow Rate
dOrifice Diameter
AOrifice Area
rhoFluid Density
gGravity
Delta pPressure Drop Across Orifice
hDriving Head
C_dDischarge Coefficient

Variables & Units

Symbol	Variable	Description	Common Units
Q	Flow Rate	Volumetric liquid flow rate through the orifice.	L/s, m³/h, US gpm
d	Orifice Diameter	Effective diameter of the sharp-edged round opening.	mm, in, m
A	Orifice Area	Cross-sectional opening area of the orifice, equal to pi d² / 4.	mm², cm², m²
rho	Fluid Density	Mass density of the liquid flowing through the orifice.	kg/m³, g/cm³, lb/ft³
g	Gravity	Local gravitational acceleration magnitude used in head-based mode.	m/s², ft/s², g
Delta p	Pressure Drop Across Orifice	Differential pressure drop across the orifice opening itself.	kPa, bar, psi
h	Driving Head	Liquid head available to drive flow through the orifice in head-based mode.	m, ft, in
C_d	Discharge Coefficient	Empirical coefficient that corrects ideal orifice discharge to actual flow.

How to Use This Calculator

01Choose the basis first. Use Pressure-Based when the orifice is driven by a known differential pressure drop across the opening. Use Head-Based when the orifice is driven by a known liquid head.
02Select which quantity to solve for: flow rate, orifice diameter, pressure drop or head, or discharge coefficient.
03Enter a discharge coefficient that matches your orifice geometry and test data whenever possible. This page does not estimate C_d automatically, and arbitrary C_d choices can materially skew the result.
04Use C_d around 0.60-0.65 only as a rough starting point for a sharp-edged thin-plate liquid orifice; rounded nozzles, valves, and pipe fittings can behave differently.
05Use pressure drop as the differential across the orifice itself, not the total line pressure or vessel pressure alone.
06If a back-calculated discharge coefficient comes out above 1, treat that as a sign that the entered flow, head, pressure drop, or diameter are inconsistent with this simplified model.
07Use this page for incompressible single-phase liquid estimates. Gas flow, flashing flow, cavitation, and certified custody-transfer orifice-meter calculations require more detailed models.

How the Formula Works

The simplified liquid-orifice equation starts from the ideal velocity predicted by Bernoulli's principle for a pressure or head difference across an opening. Multiplying the ideal result by a discharge coefficient accounts for vena contracta effects and other real-flow losses. In pressure form, the calculator uses Q = C_d A √(2 Δp / ρ), where A is the orifice area, Δp is differential pressure drop, and ρ is liquid density.

When the driving force is expressed as head instead of pressure, the same idea becomes Q = C_d A √(2 g h). Because area varies with the square of diameter, small diameter changes produce large flow changes. The accuracy of any result depends strongly on whether the chosen discharge coefficient actually matches the installed orifice geometry and flow regime.

Worked Example 01

Flow rate from pressure drop across a sharp-edged orifice

Known

Discharge Coefficient (C_d): 0.61
Orifice Diameter (d): 25 mm
Fluid Density (rho): 1000 kg/m³
Pressure Drop Across Orifice (Delta p): 50 kPa

Formula

Q = C_d A √(2 Delta p / rho)

Substitution

Q = 0.61 x (pi x 0.025² / 4) x √(2 x 50,000 / 1000)

Result

Q ≈ 0.002994 m³/s (10.78 m³/h)

For water flowing through a 25 mm sharp-edged orifice with a 50 kPa differential, the estimated liquid flow is about 10.78 cubic meters per hour when C_d = 0.61.

Worked Example 02

Required orifice diameter from target flow and head

Known

Flow Rate (Q): 27.45 m³/h
Discharge Coefficient (C_d): 0.62
Gravity (g): 9.81 m/s²
Driving Head (h): 2 m

Formula

d = √(4 Q / (pi C_d √(2 g h)))

Substitution

d = √(4 x 0.007626 / (pi x 0.62 x √(2 x 9.81 x 2)))

Result

d ≈ 0.0500 m (50.0 mm)

To pass about 27.45 cubic meters per hour under 2 meters of head with C_d = 0.62, the opening should be about 50 mm in diameter.

Worked Example 03

Discharge coefficient from measured flow and head

Known

Flow Rate (Q): 3.402 m³/h
Orifice Diameter (d): 20 mm
Gravity (g): 9.81 m/s²
Driving Head (h): 1.2 m

Formula

C_d = Q / (A √(2 g h))

Substitution

C_d = 0.0009451 / ((pi x 0.02² / 4) x √(2 x 9.81 x 1.2))

Result

C_d ≈ 0.620

Using the measured liquid flow and available head, the implied discharge coefficient at that operating point is about 0.62.

Applications

01Preliminary sizing of liquid discharge openings and restriction plates where a known discharge coefficient is available
02Checking whether a proposed orifice diameter can deliver a target liquid flow under a known differential pressure or head
03Back-calculating the implied discharge coefficient from measured liquid test data

Typical Liquid Densities for Orifice Flow Estimates

Liquid	Density (kg/m³)
Fresh water (4°C)	1000
Sea water (0°C)	1030
Light mineral oil	850
Glycerin	1260

Assumptions

01The flow is treated as single-phase, incompressible liquid flow through a round sharp-edged orifice.
02The discharge coefficient is assumed known and constant for the operating point entered.
03Head-based mode assumes the entered driving head is the effective head available at the orifice.

Where This Model Stops

01Not intended for gas flow, compressible flow, flashing two-phase flow, cavitation-limited discharge, or choked-flow analysis.
02Not a full ISO 5167 orifice-meter calculation; the page does not model beta ratio, pipe diameter effects, pressure-tap geometry, expansion factor, or installation uncertainty.
03Does not select a stocked orifice plate, account for erosion/corrosion, or check whether the downstream pressure stays above vapor pressure.
04Results can be materially wrong if the chosen discharge coefficient does not match the actual orifice geometry and Reynolds-number range, or if users apply this liquid-only model to a broader orifice-meter problem.

References

[1]
ISO 5167-1:2022 - General Principles and Requirements
ISO
Defines the general scope and operating limits for differential-pressure flow devices, including the requirement that flow remain single-phase and subsonic for ISO 5167 applications.
[2]
Propagation of Error for Many Variables
NIST/SEMATECH e-Handbook of Statistical Methods
Shows the standard orifice-meter measurement equation structure, including discharge coefficient, density, differential pressure, and beta-ratio dependence.
[3]
A Data-Driven Predictor of the Discharge Coefficient of Orifice Plates
NIST
Explains that discharge coefficient depends on the orifice and pipe geometry and the Reynolds number, which is why this simplified calculator requires user-supplied C_d.

Frequently Asked Questions

What pressure should I enter in pressure-based mode?

Enter the differential pressure drop across the orifice itself, not the upstream absolute pressure by itself. The equation uses the pressure difference that drives flow through the opening.

Can I use this for gases or steam?

No. This calculator is limited to incompressible single-phase liquid estimates. Gas and vapor flow can become compressible or choked, which requires different equations and often an expansion-factor correction.

Is this the same as an ISO 5167 orifice-meter calculation?

No. ISO 5167 orifice-meter work includes additional geometry and installation requirements, such as beta ratio, pipe diameter, pressure-tap details, and discharge-coefficient correlations. This page is a simplified sharp-edged liquid-orifice calculator with user-entered C_d.

What does it mean if the calculated discharge coefficient is above 1?

For this simplified model, a discharge coefficient above 1 means the entered flow, diameter, and driving pressure or head are not physically consistent with the assumptions used here. Recheck the measurements, units, and whether a different flow model is needed.

How is this different from the Flow Rate Calculator?

The Flow Rate Calculator uses Q = A × v when velocity is already known. This Orifice Flow Calculator estimates velocity from pressure drop or head, then applies discharge coefficient to account for real orifice losses.

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