36 



CONCLUSION 



We have shown how the force and moment acting on a body with an arbitrary m.otion 

 through a fluid subject to a time varying potential flow can be found if the body can be repre- 

 sented by a system of singularities placed within the body. 



The force can be considered to consist of three components. The first, which would be 

 the total force if the instantaneous flow were steady, is simply the "Lagally force." This is 

 found in terms of general singularities (Equations [20] and [30]). The second component de- 

 pends upon the change with timio of the singularity system generating the surface of the Dody. 

 This force (Equations [32] and [39]) is found to be a function of the strength and orientation 

 of the sources and doublets in the singularity system out not of the higher order singularities. 

 The third component is the force which would Le required to generate the given motion of the 

 body in a vacuum, if the body were to have the same density as the fluid (Equations [8] and 

 [48]). 



The moment similarly consists of the "Lagally moment" (Equations [56] and [60]) and 

 additional components, but it has not been possible to resolve these additional moments in the 

 same manner as for the force. They consist of two terms; the first, appearing in Equation [9], 

 is simple enough, but the second requires the evaluation of a surface integral (Equation [54b]). 

 However, the integrand is linear, so it is permissible to superimpose potential flows which 

 satisfy the boundary conditions. 



ACKNOWLEDGMENTS 



The assistance of Mrs. Alice Thorpe has been of great value in the preparation of this 

 report. She aided in the reduction of the many integrals and carefully checked the algebraic 

 operations, greatly increasing the author's confidence in the results. The author is also very 

 grateful to Mr. P. Eisenberg and Mr. M. Tulin for their careful review of the report. 



