Problem Statement

PRODUCT: AFT Arrow

MODEL FILE: AroVerify7.ARO

REFERENCE: Crane Co., Flow of Fluids Through Valves, Fittings, and Pipe, Technical Paper No. 410, Crane Co., Joliet, IL, 1988, Page 4-14, example 4-22

GAS: Air

ASSUMPTIONS: Example does not specify the heat transfer conditions. The AFT Arrow model assumes adiabatic.

RESULTS:

DISCUSSION:

Crane does not make a distinction between static and stagnation pressure, and it appears that static pressure is usually assumed. From the problem description, the static pressure is clearly appropriate.

The predicted flow rates agree very closely.

The Crane prediction indicates that this pipe will have subsonic velocity at the exit and hence will not choke. However, a more proper formulation of this problem shows a different mass flow will occur. This is a good example of the limitations of simplified methods such as Crane. The discrepancy comes from how to handle the exit loss of the air as it discharges to atmosphere. The Crane solution takes the appropriate K factor, equal to 1, and lumps it together with the pipe friction to obtain an overall K factor of 7.04. However, if the K factor is applied at the discharge tank and not averaged along the pipe, the mass flow differs from that calculated by Crane. The predicted flow rate using this method is 64.4 scfm. This is not drastically different from Crane’s prediction, and well within typical engineering uncertainty. But the difference, which is small here, could be larger in other applications.

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