3.7 Measurements in Ducts
83
Table 3.1 Log-Tchebycheff
rule for ducts of circular
section
Number of points Position relative to inner wall
6
0.032, 0.135, 0.321, 0.679, 0.865, 0.968
8
0.021, 0.117, 0.184, 0.345, 0.655, 0.816,
0.883, 0.981
10
0.019, 0.153, 0.217, 0.361, 0.639, 0.783,
0.847, 0.923, 0.981
3.7.2 Ducts of Rectangular Section
A variant of the log–Tchebycheff method can be used for rectangular ducts (Table 3.2
and Fig. 3.18).
Thus:
• Less than 76.2 cm: 5 points,
• 76.2–91.44 cm: 6 points, and
• Greater than 91.44 cm: 7 points.
In some texts on fluid mechanics, ducts are broken down into between 16 and
64 rectangles with the same area (Fig. 3.19) and the average is calculated. With this
configuration, a minimum of 25 points should ideally be selected (Macferran 1999).
Table 3.2 Log-Tchebycheff
rule for ducts of rectangular
section
Number of points Position relative to inner wall
5
0.074, 0.288, 0.500, 0.712, 0.926
6
0.061, 0.235, 0.437, 0.563, 0.765, 0.939
7
0.053, 0.0203, 0.366, 0.500, 0.634, 0.797,
0.947