## Introduction

Pitot tubes are used in a variety of applications for measuring fluid velocity. This is a convenient, inexpensive method for measuring velocity at a point in a flowing fluid. Pitot tubes (also called pitot-static tubes) are used, for example, to make airflow measurements in HVAC applications and for aircraft airspeed measurements.

## Static Pressure, Stagnation Pressure and Dynamic Pressure – Definitions

Understanding of the terms, static pressure, stagnation pressure and dynamic pressure is very helpful in the explanation of pitot tubes, so they are being defined in this section.

**Static pressure** is what is commonly called simply the pressure of the fluid. It’s a measure of the amount that fluid pressure exceeds local atmospheric pressure. It is measured through a flat opening that is parallel with the fluid flow. Static pressure measurement is illustrated with the first U-tube manometer in the diagram at the left.

** Stagnation pressure **is also a measure of the amount that fluid pressure exceeds local atmospheric pressure, but it includes the effect of the fluid velocity converted to pressure. It is measured through a flat opening that is perpendicular to the direction of fluid flow and facing into the fluid flow. Stagnation pressure (also called total pressure) measurement is illustrated with the second U-tube manometer in the diagram at the left.

**Dynamic pressure **(also called velocity pressure) is a measure of the amount that the stagnation pressure exceeds static pressure at a point in a fluid. It can also be interpreted as the pressure created by reducing the kinetic energy to zero. Its measurement is illustrated with the third U-tube in the diagram at the left.

## Static Pressue, Stagnation Pressue and Dynamic Pressure – Relationships

The symbol, P, is often used for static pressure. Dynamic pressure is given by the expression, ½ ρV^{2}. The stagnation pressure is then given by the following equation:

P_{stag} = P + ½ ρV^{2} + γh

Where: ρ is the fluid density (slugs/ft^{3}), γ is the specific weight of the fluid (lb/ft^{3}), h is the height above a specified reference plane (ft), V is the average velocity of the fluid (ft/sec). With the specified units for the other parameters, pressure will be in lb/ft^{2}.

## Velocity Measurement with a Pitot Tube

For pitot tube measurements and calculations, the reference plane is taken to be at the height of the pitot tube measurements, so the equation for stagnation pressure becomes:

P_{stag} = P + ½ ρV^{2} , which can be rearranged to: V = (2ΔP/ρ)^{1/2}

Where ΔP = P_{stag} – P.

The pressure difference, Δp, (or P_{stag} – P), can be measured directly with a pitot tube like the third U-tube in the figure above, or with a pitot tube like that shown in the figure at the right. This is a concentric pitot tube. The inner tube has a stagnation pressure opening (perpendicular to the fluid flow) and the outer tube has a static pressure opening (parallel with the fluid flow).

## Example Calculation

Consider a pitot tube being used to measure air velocity in a heating duct. The air is at 85 ^{o}F and 16 psia. The pitot tube registers a pressure difference of 0.021 inches of water (P_{stag} – P). Calculate the velocity of the air at that point in the duct?

Solution: Convert the pressure difference of 0.021 inches of water to lb/ft^{2} (psf) using the conversion factor, 5.204 psf/in water.

0.021 inches of water = (0.021)(5.204) psf = 0.1093 psf

The density of air at 85^{o}F and 16 psia can be calculated using the ideal gas law, to be 0.002468 slugs/ft^{3}.

(See the article, "Use the Ideal Gas Law to Find the Density of Air at Different Pressures and Temperatures," for more information.)

Now V can be calculated: V = (2ΔP/ρ)^{1/2} = [(2)(0.1093)/0.002468] ^{1/2} = **9.41 ft/sec**

## Summary

For a fluid with known density and measured difference between stagnation pressure and static pressure (ΔP), as measured with a pitot tube, the fluid velocity can be calculated with the equation: V = (2ΔP/ρ)^{1/2}.