Orifice and Nozzle Flow Calculator

The volume and mass flow through an orifice or nozzle from the pressure difference across it.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Flow through a small opening is driven by the pressure difference. The ideal speed from Bernoulli's equation is √(2 Δp / ρ). A discharge coefficient Cd, about 0.6 for a sharp-edged orifice and close to 1 for a smooth nozzle, accounts for the contraction of the jet and the losses.

The flow is Q = Cd A √(2 Δp / ρ). The equation is for a liquid or for a gas at a small pressure ratio. Compressible, choked flow needs a different method.

Formulas used

  • Q = C_d A \sqrt{\frac{2\,\Delta p}{\rho}}
  • \dot m = \rho Q

Worked example

With the default numbers in the calculator above:

  1. Orifice area: 491 mm²
  2. Ideal jet speed (Bernoulli): 10 m/s
  3. Volume flow: 3 L/s
  4. Mass flow: 2.99 kg/s

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What discharge coefficient should I use?

About 0.6 for a sharp-edged orifice in a plate, 0.8 to 0.98 for a nozzle. Use the supplier or standard value if you have one.

Does it work for air?

Roughly, when the pressure drop is small compared with the absolute pressure. For large drops the flow chokes and needs compressible flow equations.

What pressure drop do I use?

The difference between the pressure before and after the orifice, measured across it.

Related calculators

Further reading: White, Fluid Mechanics; Munson, Young and Okiishi, Fundamentals of Fluid Mechanics; Crane Technical Paper 410.

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