# Principle of the integrating pitot tube

Integrating pitot tubes are used for the flow measurement of gaseous or liquid fluids such as combustion air, compressed air, natural gas, steam, water etc. in pipes and channels. Pitot tubes have several tappings with and against the direction of flow.

At the tapings against the direction of flow a dynamic positive pressure pdyn1 stagnation pressure develops, at the openings in direction of flow a dynamic negative pressure pdyn2 is developing.

Within the pitot tube the pressures of the tappings are averaged and measured outside of the pitot tube. From the measure dp one can calculate the flowrate in the pipe.

dp = p1 - p2
p1 = pstat + pdyn1
P2 = pstat + pdyn2
dp = pdyn1 - pdyn2

## calculation basics of dp measurement

the basic formula of dp flow measurement is deduced from the law of the conservation of energy. From the dp one can calculate the massflow in the pipe:

qm=K*pi*d^2/4*epsilon*(2*dp*rho)^0.5

qm – mass flow
K – calibration contstant of dp element (K-Number)
d – inside diameter of pipe
epsilon– expansion coefficient
dp – measured differential pressure
rho – density of fluid

The dimensionless calibration constant K is determined by the different manufacturers of averaging pitot tubes and communicated to the user. A typical value is .62 to .68.

The expansion factor epsilon corrects the change in density of the fluid by the pressure loss of the integrating pitot tube. For incompressible fluids (liquids), epsilon = 1, for compressible fluids epsilon is less than 1, but typically remains in the range [0.97 <epsilon <1]. The density rho is the density of the fluid immediately before the integrating pitot tube (rho1).

### flow calculation identical with ISO 5167

The calculation basics with pitot tubes is virtually identical, with the calculation basis of the classical primary elements such as orifice, venturi or nozzle. These are described in detail in ISO 5167. The only difference in the formula for calculating the mass flow is the first part of the equation: While the dynamic pressure probe uses here the calibration constant K primary elements are using a fraction in which the diameter ratio beta and the discharge coefficient C are included.

Since the mass flow calculation is -beside the constant part of the equation- identical, pitot tubes can be carried out by most flow computers or computing modules in process control systems. A manual programming is usually not necessary.

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 Fluids Gas, Steam Liquids Pipe Sizes 1..25 mm deltaflow DF8 20..100mm deltaflow DF12 80..2500mm deltaflow DF25 200..15000mm deltaflow DF44 Operating conditions –200 bis zu 1240 °C 0..690 bar Pure to extremely contaminated, aggressive media Eex ia, ATEX Certificates ATEX PED 97/23/EC, TRD 2.2 / 3.1 / 3.2 (EN 10204)

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