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Design of Flow Systems 441

Figure 8.2.1 An orifice meter with corner pressure taps. Adapted from
Ref. 26 with permission.

Variable-Area Meters

To size a rotameter requires calculating the volumetric flow rate of a standard fluid
at standard conditions. Most manufacturers calibrate rotameters using a stainless-
steel float and water at a standard temperature for liquids and air at a standard
temperature and pressure for gases. For other fluids, float materials, and operating
conditions, the flow rate must be converted to an equivalent flow rate of water or
air. To derive a formula for making this conversion, Bernoulli's equation is ap-
plied across the float shown in Figure 8.15 to give Equation 8.9.
Because a rotameter tube is tapered, the annular flow area varies with posi-
tion of the float, as shown in Figure 8.15. The conservation of mass for an incom-
pressible fluid becomes

AiVi =A 2 v 2 = AoVo (8.15)

where the subscript 1 refers to the entrance of the rotameter, 2 the exit of the me-
ter, and o to the annular area between the float and tube.
The friction loss term,
2
Kv 0
E = —— (8.16)
2 Be

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