PROPERTIES & CHARACTERISTICS
MACH NUMBER RANGE
The lower usable limit for Pitot-Static probes depends on the sensitivity of the readout device used with the probe. A differential pressure of 1" of water, for example is about the minimum that can be measured with 1% accuracy with ordinary slant gauges, so the lower limit is approximately at a Mach Number of 0.06 or velocity of 70 ft/sec for air at standard atmospheric conditions. While there is no minimum Mach Number for the probe itself, there are viscous drag effects that should be considered when using a probe in a low velocity fluid field. (See Reynolds Number Range). The upper limit is at about Mach 0.95 for the total pressure reading and 0.70 for the static as shown in Figure 1. The static reading is accurate to 0.5% to a Mach Number of 0.50 and to 1.5% up to Mach 0.70. At this point the calibration becomes erratic due to the formation of local shock waves on and around the tip of the probe and the reading can vary as much as 10% with slight changes in flow conditions or proximity to solid boundaries. Above Mach 1.0 both the total and static readings vary considerably from true stream values but they can be corrected theoretically.
Figure 1. Mach Number Range.
|Pt||Total pressure (impact / stagnation pressure)|
|Ps||Static pressure (ambient / stream pressure)|
|Ptp||Indicated total pressure|
|Psp||Indicated static pressure|
The static pressure indication is sensitive to distance from solid boundaries. Figure 3 shows how this error increases the indicated velocity pressure at a Mach Number 0.25. The probe and boundary form a Venturi passage, which accelerates the flow and decreases the static pressure on one side. The curve shows that static readings should not be taken closer than 5 tube diameters from a boundary for 1% accuracy and 10 tube diameters is safer.
Figure 3. Boundary Effects.
REYNOLDS NUMBER RANGE
Pitot-Static probes are not directly affected by Reynolds Number except at very low velocities. Therefore, in liquids where compressibility effects are absent, their calibration is substantially constant at all velocities. The minimum Reynolds Number for the total pressure measurement is about 30 where the characteristic length is the diameter of the impact hole. Below this value the indicated impact pressure becomes higher than the stream impact pressure due to viscosity effects. This error is only noticeable in air under standard atmospheric conditions for velocities under 12 ft/sec with impact holes 0.010" diameter or less.
YAW AND PITCH ANGLE RANGE
If the fluid stream is not parallel to the probe head, errors occur in both total and static readings. These are the most important errors in this type of instrument because they cannot be corrected without taking independent readings with another type of probe.
Figure 2. Yaw and Pitch Angle Error.
|VP||Indicated velocity calculated from Ptp and Psp using standard equations.|
|W||Weight flow rate - lbs. sec x ft²|
|Wp||Indicated weight flow rate from Ptp and Psp|
Note that yaw and pitch angle affect the readings exactly the same. The errors in total and static pressure increase quite rapidly for angles of attack higher than 5°, but they tend to compensate each other so the probe yields velocity and weight flow readings accurate to 2% up to angles of attack of 30°. This is the chief advantage of the Prandtl design over other types.
Pitot-Static tubes appear to be insensitive to isotropic turbulence, which is the most common type. Under some conditions of high intensity, large scale turbulence, could make the angle of attack at a probe vary over a wide range. This probe would presumably have an error corresponding to the average yaw or pitch angle produced by the turbulence.
The speed of reading depends on the length and diameter of the pressure passages inside the probe, the size of the pressure tubes to the manometer, and the displacement volume of the manometer. The time constant is very short for any of the standard tubes down to 1/8" diameter; however, it increases rapidly for smaller diameters. For this reason 1/16" OD is the smallest recommended size for ordinary use - this will take 15 to 60 seconds to reach equilibrium pressure with ordinary manometer hook-ups. These tubes have been made as small as 1/32" OD, but their time constant is as long as 15 minutes and they clog up very easily with fine dirt in the flow stream. If very small tubes are required, it is preferable to use separate total and static tubes rather than the combined total-static type. Where reinforcing stems are specified on small sizes, the inner tubes are enlarged at the same point to ensure minimum time constant.
Probes are installed in the fluid stream with the impact hole facing upstream, the head parallel to the flow direction and the stem perpendicular. Types PA and PB (Fig. 4) are well suited to mounting on thin - walled ducts where the probe is to be inserted from the outside. Types PC and PD (Fig. 5) are designed with removable pressure take-offs. This allows for installation from within the duct where it is not practical to make an insertion hole diameter equal to the length of the probe tip. Figure 6 shows a correlation between probe diameter and minimum wall insertion dimensions for a probe with fixed take-offs.
Figure 4. Thin wall installation.
Figure 5. Thick wall installation.