11. Point Velocity Area Methods

Computing discharge point velocities for open channel flow is discussed in chapter 10. In conduits, several point velocities can be obtained by traversing with a velocity measuring device such as a pitot tube. Arrays of several velocity measuring devices, such as axial current meters, are sometimes fixed on racks that span the conduit to measure several velocities simultaneously. Some flowmeters directly measure average velocity along lines through the flow.

The measurement of point velocities is relatively simple. However, partitioning the flow section relative to velocity points is complex, depending on the accuracy desired. The main problem in determining proper partial areas is that each point velocity represents or determines meaningful velocity weighting factors related to each point location. Many schemes can be used to locate measuring points on grids or diameters and assign weighting factors for each position. The procedures are further complicated when corrections are needed to account for the obstruction of rack support systems and the size of the instruments themselves. If accuracies better than +/-3 percent are needed, then procedures set by codes such as ISO (1977) and ASME (1992) should be consulted.

Some methods of averaging velocity are done by selecting equal areas related to the shape of the flow cross section and measuring velocity at specific points within these areas. For pitot measure-ments, the average of the square root of the velocity heads of the point measurements is multiplied by the flow section area.

The most common pressure conduit is the circular pipe. For a constant rate of flow, the velocity varies from point to point across the stream, gradually increasing from the walls toward the center of the pipe. The mean velocity is obtained by dividing the cross-sectional area of the pipe into a number of concentric, equal area rings and a central circle. The standard (ASME, 1983) 10-point system is shown on figure 14­10a. More equal area divisions may be used if required by large flow distortions or other unusual flow conditions. Velocity measurements are taken at specific locations in these subareas (figure 14-10a) and are adjusted in terms of average velocity head by the equation:

Figure 14-10 -- Locations for pitot tube measurements in circular and rectangular conduits (reproduced from British Standard 1042, Flow Measurement [1943], by permission of the British Standards Institution).

The mean velocity in rectangular ducts can be found by dividing the cross section into an even number (at least 16) of equal rectangles geometrically similar to the duct cross section and measuring the velocity at the center of each area (figure 14-9b). Additional readings should be taken in the areas along the periphery of the cross section according to the diagram on figure 14-9c. Then, the average velocity is determined from equation 14-5.

Acoustic devices, discussed in chapter 11, measure accurate average velocity along chords or diametral lines in planes across the flow section. The diametral arrangement uses the simple average of the line velocities corrected for the angle of the plane across the conduit. The multiple chordal systems use a specific weighting factor for each line velocity to determine the average (AMSE, 1992). The chord locations are specified to maximize accuracy.