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About the Tool

The tool RD-04 computes the dynamic coefficients of liquid annular seal using Black's model.

In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.


Liquid Annular Seal (Black Model)

The input in the toolbox is

After clicking "Run", the results will be shown as follows in another page.

Kxx=Kyy=  6912209.40233639  N/m

Kxy=-Kyx=  6872962.45169094  N/m

Cxx=Cyy=  109386.59478716  N-s/m

Cxy=-Cyx=  9354.76593832  N-s/m

Mxx=Myy=  74.44286203  N*s^2/m

Subject Review

Liquid Annular Seal (Black Model)

Black model of liquid annular seals is developed based on Lomakin's theory. Due to the Bernoulli effect during the leakage process, radial forces are generated to support the rotation shaft in pumps.

For small whirl motion around a centered position, the linearized forces acting on the rotor are


Kxx=Kyy: Direct Stiffness

Kxy=Kyx: Cross-coupled Stiffness

Cxx=Cyy: Direct Damping Coefficient

Cxy=Cyx: Cross-coupled Damping Coefficient

Mxx=Myy: Mass Inertial


1. D. Childs, Turbomachinery Rotordynamics: Phenomena, Modeling, & Analysis, 1993, John Wiley & Sons Inc, New York.

2. W.J. Chen and E.J. Gunter, Introduction to Dynamics of Rotor-Bearing Systems, 2007, Trafford Publishing.