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CHAPTER 14 - MEASUREMENTS IN PRESSURE CONDUITS
10. Pitot Tube Velocity Measurements
The straight upstream tube shown on figure 14-9a, which is connected perpendicular and flush to the inside wall of the pipe so it does not sense any velocity force, is a called a piezometer. Water rises in the piezometer to an elevation that only balances the pressure head in the conduit. A simple pitot tube is shown downstream on figure 14-9a. This open tube has a right-angle bend that is inserted into conduit flow with its horizontal leg pointed upstream and parallel to velocity. Water runs into the tube and rises into the vertical stem until its weight balances both the force of the pipeline pressure head, hp, sometimes called static head, and the force of approach velocity that has been converted to velocity head, hv, by stagnation at the tip. In this form, the pitot tube is sometimes called a total head tube because the water rises above the tip a height equal to the sum, Ht, of pressure head in the conduit plus velocity head.
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For a velocity measurement, the pressure head is subtracted from the total head, Ht, resulting in velocity head, hv, or V 2/2g. Solving for the velocity of flow, V, results in:
where:
V = velocity
g = gravity constant
hv = measured velocity head
C = coefficient
For total head tubes that have reasonably long horizontal legs relative to tube diameter, the tube coefficient is commonly unity. However, pitot tubes with damaged tips, short tips, tube burrs, and short tips need calibration checks to determine correct tube coefficients that may deviate considerably from unity.
A more complex form of pitot tube is known as the pitot-static tube, which consists of the total head tube threaded through the center of a larger tube. Static ports are drilled perpendicular to and around the circumference of the horizontal part of the outer tube. Typical pitot-static tubes have static ports that are placed a distance of at least three outer tube diameters from the tip and at least eight diameters from the vertical leg of the outer tube (figure 14-9b). These distances protect the static ports from stem and tip disturbances, which would cause tube coefficients to deviate from unity.
Properly constructed and undamaged standard pitot-static tubes have a coefficient very close to unity and can be used without corrections for tube interference effects (ASME, 1983). Some special instruments have coefficients that differ considerably from unity. Appropriate coefficients should be applied as specified by manufacturers.
Manometers are commonly used to measure heads separately or differentially in a U-tube. The suction lift manometer shown in figure 14-9c uses an inverted U-tube with partial vacuum to lift the water surfaces up to the scale for reading the pressures where pipeline total head is insufficient to do so itself. The velocity head is obtained by subtracting the pressure head from the total head. More conveniently, a differential pressure cell that senses velocity head directly can be used. A recording digital voltmeter attached to the pressure cells can provide continuous records of velocity.
The rate of flow in pipelines under pressure may be computed from the conduit cross-sectional area and velocity observations made by pitot tubes or by commercial adaptations of pitot tubes (ASME, 1983; 1992). Reinforced pitometers have been used successfully in pipes up to 5 feet (ft) in diameter with flow velocities of 5 to 20 ft/s. Even large pipes can be traversed by having access ports on both sides of the pipe and probing to or past the conduit centerline from each side. The principal disadvantage encountered is that relatively large forces push on the tube when flow velocities are high, making positioning and securing of the instrument difficult. Dynamic instability may also occur, causing the tube to vibrate and produce erroneous readings. The flow measurements can be very accurate at moderate flow velocities.
