ON HYDRODYNAMIC MASSES 



by 



Georg P. Weinblum, D.Eng. 



The present synopsis is the English version of a paper in German 

 presented on the sixtieth birthday of Professor Schnadel in Hamburg. Although 

 it contains only a few original contributions by the author, it has been de- 

 cided to publish the review as a TMB report in order that it may serve as an 

 introduction to a subject which, despite its importance in many fields of 

 hydrodynamics, has been somewhat neglected in the past. 



In the present paper, we shall treat the problem of the hydrodynamic 

 (added) masses of bodies which, like the ship, move through the free surface 

 of the water. While for bodies in a medium extending infinitely in all direc- 

 tions the hydrodynamic inertia factors are defined purely geometrically ex- 

 cept for the density of the medium, in our case dependencies on various quan- 

 tities such as the Froude number, an acceleration ratio, a frequency para- 

 meter, etc., can appear. The nature of these dependencies is known only in a 

 general way. It is the purpose of this study to give a review of the status 

 of our knowledge in this field. 



1 • THE KELVIN FLOW FIELD 



1 .1 The study of the motion of a ship in water must, at the present, 

 be carried out in various degrees of approximation. We shall assume here 

 as an hypothesis that: the fluid is ideal, extends infinitely in all direc- 

 tions, and the flow in it is caused only by the motion of the body. 



A "regular" (simply connected) body then produces an irrotational 

 and acyclic velocity field which is characterized by a velocity potential <p 

 and which, indeed, is also called the classical Kelvin field. 1 According to 

 Kirchhoff , the kinetic energy of this field is given by a quadratic form in 

 the velocity components of the body with the hydrodynamic (added) masses as 

 the coefficients. The forces exerted by the fluid on the body can be defined 

 by means of the hydrodynamic masses without performing the troublesome inte- 

 gration of the pressures over the body. 



As usual we snail define the apparent or virtual mass in a given 

 direction as the sum of the mass of the body m plus the hydrodynamic mass 

 in that direction; we shall here set m equal to the mass of the displaced 



References are listed on page 14. 



