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Measuring wind speed

Air and fluids · level 6, lesson 4 of 6

A question to start

An aircraft measures its airspeed with a small tube pointing forward into the wind. How can a tube measure speed?

The idea

Air that rushes straight into the open end of a forward-facing tube is brought to a stop. By Bernoulli's principle, its pressure rises by the dynamic pressure. A second opening on the side feels only the ordinary pressure of the passing air. The difference is

\[\Delta p = \tfrac12 \rho v^2 \quad\Rightarrow\quad v = \sqrt{\frac{2\,\Delta p}{\rho}}.\]

This is a Pitot tube. To get the speed from it, you must know the air's density.

windfront: air stops,high pressureside: ordinarygauge
Speed for a 50 Pa reading Mars Earth
Air density 0.016 kg/m³ 1.217 kg/m³
Wind speed 79 m/s 9.1 m/s

On Mars, the same pressure reading means a far faster wind, and an everyday breeze gives only a fraction of a pascal. That is why Mars wind sensors must be very sensitive. Perseverance's weather station, MEDA, measured a 5.7 m/s wind just before a dust devil passed over the rover.

Worked examples

1. Earth, 50 Pa. \(v = \sqrt{2 \times 50/1.217} = \sqrt{82.2} = 9.1\) m/s.

2. Mars, 50 Pa. \(v = \sqrt{2 \times 50/0.016} = \sqrt{6250} = 79\) m/s.

3. MEDA's 5.7 m/s wind. \(\Delta p = \tfrac12 \times 0.016 \times 5.7^2 = 0.26\) Pa: about 2.6 millionths of Earth's sea-level air pressure.

Try it

  1. What does a Pitot tube measure directly?
  2. A Pitot tube on Earth reads 200 Pa. Find the airspeed.
  3. The same reading on Mars. Find the airspeed.
  4. Why must a pilot's airspeed reading be corrected at high altitude?
Answers
  1. The difference between the stopped-air pressure and the ordinary pressure.
  2. \(\sqrt{400/1.217} = 18\) m/s.
  3. \(\sqrt{400/0.016} = 158\) m/s.
  4. The air is less dense up there, so the same pressure reading means a faster speed.

Common mistake

Forgetting the square root. Doubling the pressure reading does not double the speed: it multiplies it by \(\sqrt2 \approx 1.41\).

Where it leads