Pitot Tube Calculator: v = sqrt(2 dp / rho)

How fast a fluid flows, from the pressure difference measured by a Pitot tube.

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

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • v = \sqrt{\frac{2\Delta p}{\rho}}
  • \Delta p = \tfrac12\rho v^2

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the flow speed: flow speed = (sqrt(2) x dynamic pressure (stagnation minus static)^0.5) / (density of the fluid^0.5)
  2. Put the values in (every value in its SI unit): flow speed = (sqrt(2) x 600^0.5) / (1.204^0.5)
  3. The answer: flow speed: 31.5702 m/s
  4. The same answer in other units: 113.653 km/h; 61.3676 knots

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

Common questions

How does a Pitot tube work?

It measures the stagnation pressure at the tip and the static pressure on the side. The difference is the dynamic pressure, which gives the speed.

Why does density matter?

The same pressure difference means a higher speed in a lighter fluid, so the density of the air at your height and temperature is needed.

When is the formula wrong?

At speeds above about 100 m/s in air, where compressibility changes the result.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics text (Bernoulli's equation, Pitot tubes).

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