Calculation Basics for Differential Pressure

Principle of the integrating averaging 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 develops. Within the pitot tube the pressures of the tappings are averaged and measured outside of the pitot tube.

From the dp measurement 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 = Kε(π∕4)d2√(2.dp.ρ)

with:

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

The dimensionless calibration constant K is used by the different manufacturers for identifying their integrating pitot tubes and this is communicated to the user. A typical value is between 0.62 and 0.68.

The expansion factor ε is used to correct for density changes in the fluid for media of different properties.

For incompressible fluids (liquids), ε = 1; in compressible fluids is ε less than 1, but typically remains in the range [0.97