BIZOMAT MAKEOS · Hydraulics
Orifice and Restrictor Flow
How much liquid flows through this orifice at this pressure drop, or what drop does a flow cause?
Flow through a sharp-edged orifice, jet or restrictor from the discharge coefficient, diameter and pressure difference, or the pressure drop for a given flow.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculate | choice | Find the flow for a pressure drop, or the drop for a flow. |
| Orifice diameter | mm | Smallest diameter of the orifice. |
| Discharge coefficient | Discharge coefficient (about 0.6–0.65 for sharp-edged orifices, up to about 0.95 for rounded nozzles); measured values are best. | |
| Pressure drop | bar | Pressure difference across the orifice (flow mode). |
| Flow (pressure-drop mode) | L/min | Flow through the orifice (pressure-drop mode). |
| Fluid density | kg/m³ | Density of the fluid at the working temperature (mineral hydraulic oil about 870 kg/m³, water about 998 kg/m³). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Calculate
- What it is
- Whether to find the flow that passes for a known pressure difference, or the pressure difference a known flow creates across the orifice.
- Units and format
- Choose one of 2 options from the list: Flow from pressure drop; Pressure drop from flow.
- Example
- The form opens with “Flow from pressure drop” selected as a worked example. Choose the option that matches your case.
- Get it right
- Only the input for the chosen mode is used: pressure drop for flow, or flow for pressure drop.
What this means: Orifice diameter
- What it is
- The diameter of the narrowest part of the hole the fluid passes through: the orifice bore, restrictor jet or nozzle throat.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flow rises with the square of diameter at the same pressure drop.
- Get it right
- Use the smallest bore in the flow path, not the port or fitting size.
What this means: Discharge coefficient
- What it is
- The ratio of actual flow to the ideal flow through the same hole, allowing for the jet narrowing and friction. It depends on the edge shape and is best taken from a measurement or the restrictor maker.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.62 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flow rises in direct proportion; the pressure drop for a given flow falls with its square.
- Get it right
- Enter a fraction below one; sharp and rounded edges behave very differently.
What this means: Pressure drop
- What it is
- The difference between the pressure just upstream and just downstream of the orifice. Used only when calculating flow.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0 bar to 5000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flow rises with the square root of the pressure drop.
- Get it right
- This is a difference across the orifice, not the system gauge pressure, unless the outlet is at atmosphere.
What this means: Flow (pressure-drop mode)
- What it is
- The volume of fluid passing through the orifice each minute. Used only when calculating the pressure drop.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0 L/min to 1000000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The pressure drop rises with the square of flow.
- Get it right
- Used only in the pressure-drop mode; litres per minute, not per second.
What this means: Fluid density
- What it is
- The mass per unit volume of the fluid at its working temperature, from the fluid supplier’s data sheet.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 870 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A denser fluid passes less flow for the same pressure drop.
- Get it right
- Use density at operating temperature; it changes as oil warms.
Method and formulas
- Q = Cd × A × √(2Δp ÷ ρ), with A = πd²/4, Δp in Pa.
- Δp = ρ ÷ 2 × (Q ÷ (Cd A))².
- Example: a 2 mm orifice at 50 bar passes 12.529 L/min of oil.
Limitations
- Turbulent flow through a short orifice; at low Reynolds numbers (cold oil, tiny holes) Cd falls.
- Cavitation at large pressure drops limits the flow.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a damping or flow-control orifice
- Estimate leakage through a hole
- Check pressure drop across a jet or nozzle
Who it is for
- Hydraulic and process engineers
- Maintenance engineers
- Design engineers
What you get
- Flow
- Pressure drop
- Jet velocity
Interpreting the result
- Use a measured Cd for accurate flow control; small manufacturing changes alter Cd.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3024–3027, 352–368. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Orifice plates and differential pressure
In Flow Measurement by the Numbers
What it covers: How an orifice plate turns flow into a pressure difference, the discharge coefficient, sizing a plate, the square-root law and turndown, permanent pressure loss, and a square root left out.
Method explained here · BIZOMAT original book
Dimensions, units and the homogeneity check
In Scale Models by the Numbers
What it covers: Express engineering quantities in mass, length and time, check any formula or spreadsheet for dimensional consistency, and find the hidden constants in unit-specific formulas.
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