Rotameters Reynolds number

Values of Cd for various plummet shapes in rotameters are presented in Fig. 14-55. The Reynolds number applicable to the rotameter coefficient of discharge is based on the flow conditions through the annular opening between the plummet and the containing tube. The equivalent diameter for use in the Reynolds number consists of the difference between the diameter of the rotameter tube at the plummet location and the maximum diameter of the plummet. 

The two identical nozzles and their dimensions described previously [2] had contractions of area ratio 9.0 and followed a fifth-order polynomial [3] to a diameter of 25 mm. Fig. 6.1. The nozzle separation was varied between 0.2 and 2.0 exit diameters with bulk velocities from 1.49 to 7.00 m/s, and, since these velocities corresponded to Reynolds numbers of 2,000 and 10,000, a perforated plate was located at the end of the contraction with 4-millimeter diameter holes and 50% solidity. A subsequent straight pipe, two exit diameters in length, allowed the wakes to diminish and the small-scale turbulence to develop [4]. The two jets were mounted on a frame that allowed the separation to be varied while maintaining the same geometric axis. The compressed air and gas supply of natural methane was filtered, and the flow was measured with calibrated rotameters to accuracy better than 3%, while the centerline velocities were matched within 0.1 m/s. 

The tube can be designed such that the quadratic relationship between area and height is nearly linear. When the rotameter is calibrated for the operating conditions, the variation of the physical properties related to the Reynolds number, and hence the drag coefficient, may be lumped together to give the following relationship ... 

Correlations, dimensionless numbers, and regime maps have been developed for many of these applications. The Reynolds number was introduced in Chapter 5 to differentiate flow regimes in pipes—laminar versus transition versus turbulent. In Chapter 6, the notion of particle Reynolds number was mentioned with respect to drag force and rotameters. 

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