Appendix E 



SUMMARY OF ADDED MASS COEFFICIENTS 



The concept of added mass is well known in fluid mechanics. The physical 

 explanation of this phenomenon Is that when a body is subjected to an unbalanced 

 force, not only must the mass of the body be accelerated, but also that of the 

 added fluid mass surrounding the body. The ratio of this added fluid mass to the 

 body mass is the added mass coefficient, Cj^ . 



The added mass depends on the dimensions and shape of the body and the 

 density and viscosity of the fluid. In general, measurements of the apparent added 

 mass have been obtained under two fundamentally different flow situations. In one 

 the motion is oscillatory in that an immersed body is vibrated. In the other the 

 motion is unidirectional in that an Immersed body is accelerated recti linearly. The 

 exact analytical description of fluid resistance to the acceleration of an arbitrarily 

 shaped submerged solid Is not known, hence the exact added mass coefficient for 

 various shapes of objects Is not known. The following reports are the results of 

 different experiments under different conditions, but they are quite consistent: 

 T. E. Stelson and F. T. Mavis, °E. Silberman, 7 T. Sarpkaya, ^N, L. Ackermann 

 and A. Arbhabhirama, ° O. C. Zienkiowicz and B. Nath. 10 A summary of most of 

 the important results obtained from these references is presented in Figure E-1. 



The coefficients, C^ , have been arranged in terms of a common dimension, 

 namely the ratio of the added mass to the mass of fluid displaced. The results obtained 

 from oscillatory motion are as follows: 



1. Spheres: C^ = 0.51. This compares with a value of 0.50 obtained from 

 Ideal fluid theory for rectilinear motion. 



2. Cubes: C^ = 0.67 ("broadside -on" or "edge-on"). 



3. Circular Cylinders: See Figure E-1. The abscissa Is the ratio of length to 

 diameter. The motion Is in the direction perpendicular to the circular 

 cross section. 



4. Rectangular Plates: See Figure E-1. The abscissa Is the ratio of length to 

 width. The motion Is in the broadslde-on direction. The ratio of thickness 

 to width is limited to values less than 0.04. 



5. Square Prisms: See Figure E-1. The abscissa is the ratio of length to width 

 of the square sides. The motion is in the direction perpendicular to the 

 square cross section. 



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