Pitot tubes are commonly used to measure air velocity and calculate volumetric flow rate in heating, ventilation, and air conditioning systems. They are simple, durable sensing devices that can be connected to a differential pressure instrument to measure the pressure created by moving air.
Beyond HVAC systems, Pitot tubes are used to determine aircraft airspeed, watercraft speed, and the flow velocity of liquids, air, and other gases in industrial applications.
What is a Pitot Tube?
A Pitot tube is a fluid-velocity sensor invented by French engineer Henri Pitot during his work with aqueducts. Pitot published the design in 1732, and Henry Darcy, another French engineer, modified it into a form resembling the modern instrument in 1858.
A basic Pitot tube consists of a tube with an opening pointed directly into the oncoming fluid. When the moving fluid enters the opening, it is brought to rest because it cannot continue through the tube. The pressure produced at this stagnation point is called stagnation pressure, total pressure, or Pitot pressure.
Total pressure alone is not enough to determine velocity. Static pressure must also be measured so that the dynamic pressure created by the fluid’s motion can be calculated.
How a Pitot Tube Measures Pressure
A Pitot tube consists of two pressure passages incorporated into a single probe.
The opening at the end of the probe faces directly into the airflow and senses total pressure. Radial holes positioned along the side of the probe are perpendicular to the direction of flow and sense static pressure without receiving the full impact of the moving air.
The probe's internal passages keep these pressures separate and transfer them to two pressure connections:
- The total-pressure connection is connected to the high-pressure port of the measuring instrument.
- The static-pressure connection is connected to the low-pressure port.
The differential pressure instrument subtracts static pressure from total pressure. The resulting difference is dynamic pressure, which is also commonly called velocity pressure in HVAC applications.
Therefore:
Where:
- pt is total or stagnation pressure.
- ps is static pressure.
- pv is dynamic or velocity pressure.
How Bernoulli's Equation Relates Pressure to Velocity
Pitot tube measurement is based on Bernoulli's equation. For steady, incompressible flow along a streamline, the equation describes the relationship among static pressure, velocity, elevation, and fluid density.
When the probe brings the moving fluid to rest at its forward-facing opening, the fluid's kinetic energy is converted into pressure. This creates a total pressure that is higher than the surrounding static pressure. The difference between these pressures represents the dynamic pressure associated with the fluid's velocity:
Solving for velocity gives:
Or, using velocity pressure:
Where:
- V is the fluid velocity.
- pt is total pressure.
- ps is static pressure.
- pv is velocity pressure.
- ρ is the density of the fluid.
Fluid velocity is proportional to the square root of velocity pressure, not directly proportional to velocity pressure. For example, doubling the velocity produces four times the velocity pressure when fluid density remains constant.
These equations assume that the fluid can be treated as incompressible. Liquids can typically be treated as incompressible under ordinary operating conditions. Air and other gases may also be approximated as incompressible when velocity is sufficiently low and changes in density are negligible. Compressibility corrections may be required at higher gas velocities.
Measuring Differential Pressure
The pressure connections on the Pitot tube are connected to a differential pressure instrument, such as a liquid-column manometer, differential pressure gage, or electronic differential pressure transmitter.
A mechanical differential pressure instrument may use a diaphragm that separates the high- and low-pressure chambers. Total pressure acts on one side of the diaphragm, while static pressure acts on the other. The resulting diaphragm movement corresponds to the difference between the two pressures.
When a liquid-column manometer is used, the differential pressure is indicated by the difference in liquid-column height:
Where:
- Δp is the pressure difference between total and static pressure.
- Δh is the difference in liquid-column height.
- ρl is the density of the manometer liquid.
- g is acceleration due to gravity.
Substituting this relationship into the velocity equation gives:
This calculation converts the observed liquid-column displacement into fluid velocity while accounting for the densities of the flowing fluid and the manometer liquid.
Calculating Air Velocity from Velocity Pressure
For standard air, the general velocity equation may be simplified when velocity pressure is measured in inches of water column and velocity is expressed in feet per minute:
Where:
- V is air velocity in feet per minute.
- pv is velocity pressure in inches of water column.
- 4005 is a conversion factor based on standard-air density.
When actual air density differs from standard conditions, the calculation must be corrected:
Where d is the ratio of actual air density to standard-air density.
Temperature, atmospheric pressure, altitude, and humidity can affect air density. Accounting for these conditions becomes increasingly important when accurate velocity and flow calculations are required.
Converting Air Velocity to Volumetric Flow Rate
Once average air velocity has been determined, volumetric flow rate can be calculated by multiplying velocity by the duct's cross-sectional area:
Where:
- Q is volumetric flow rate.
- V is average fluid velocity.
- A is the internal cross-sectional area of the duct or pipe.
When velocity is expressed in feet per minute and area is expressed in square feet, the resulting flow rate is expressed in cubic feet per minute.
A Pitot tube measures velocity pressure at a specific point. Because airflow velocity is rarely uniform across an entire duct, a single reading does not necessarily represent average duct velocity. Accurate flow-rate calculations generally require a Pitot tube traverse, in which readings are collected at multiple specified locations across the duct and used to determine average velocity.
Straight duct runs and sufficient distance from elbows, dampers, transitions, fans, and other disturbances help produce a more stable velocity profile. Probe alignment is also important because the total-pressure opening must face directly into the airflow.
Using a Pitot Tube with a Differential Pressure Gage
For a typical HVAC air-velocity measurement:
- Position the Pitot tube in the duct with its total-pressure opening facing upstream.
- Connect the total-pressure fitting to the high-pressure port of the differential pressure instrument.
- Connect the static-pressure fitting to the low-pressure port.
- Read the resulting velocity pressure.
- Convert velocity pressure to air velocity using the appropriate equation or instrument scale.
- Average measurements taken across the duct when calculating volumetric flow rate.
- Multiply average velocity by the internal duct area to determine flow rate.
A manometer or Series 2000 Magnehelic® Differential Pressure Gage can display the difference between total and static pressure. Depending on the instrument and scale, the result may be displayed as velocity pressure or converted directly into air velocity.
Understanding What the Measurement Represents
A Pitot tube does not measure volumetric flow rate directly. It measures total and static pressure at a particular location. Their difference provides velocity pressure, which is used to calculate local fluid velocity.
The complete measurement path is:
Understanding this sequence is important because errors in probe position, pressure connections, fluid-density assumptions, duct-area calculations, or velocity averaging can affect the final flow-rate result.
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