Expansion Factors for Two Variable Area Flow Meters

Abstract

Data acquired in the years 1958 to 1960 at the Naval Ship Engineering Center under sponsorship of the American Society of Mechanical Engineers are used to derive semiempirical equations for the performance of two variable area meters with both liquid and gas flow. As the measurements are put to a useage for which they were not intended, the data treatment is considered illustrative of the application of a flow equation derived by an analysis based upon a force and momentum balance. The hydraulic flow coefficient is expressed in terms of a function of (a) pressure drop divided by float weight and of (b) a dimensionless length ratio β for float position. Density ratio is used to modify the function of β to derive the expansion factor Y for gas flow as suggested by the analysis. Reasonable agreement between measured and derived values of Y is demonstrated, and approximate measures of the velocity profiles in the meter are derived from the correlation equations. One set of air tests at one float position in which the viscous influence number N was changed from 500,000 to 783,000 indicated (within this range) a possible insensitivity of the derived function of β to change of N.