Sec. 623 



ESTIMATE OP ADDED LIQUID MASS 



425 



Because of the second powers involved, this 

 method requires a very careful measurement of 

 both frequencies. 



A second method, of much more general 

 application, is to develop procedures whereby 

 the added-liquid masses (and mass moments of 

 inertia) can be derived from the known values for 

 geometric shapes, as outlined in Sec. 62.2 and 

 as listed on Figs. 62.A and 62.B. For many of the 

 geometric shapes for which the velocity potentials, 

 kinetic energies of the surrounding flow, and 

 added-liquid masses are known, the lower halves 

 resemble roughly the underwater forms of ships 

 having the same size and proportions. For 2-diml 

 bodies, this resemblance applies to the immersed 

 transverse sections of the surface ships under 

 investigation; for 3-diml bodies it applies to the 

 whole underwater hull, as described for the half- 

 ellipsoid and the ABC ship of Part 4 in the pre- 

 ceding section. It is then assumed that the added 

 mass of the liquid surrounding the immersed 



section or hull of the ship is one-half of the value 

 calculated for the whole geometric section or 

 geometric form far below the surface. For example, 

 if 2a is taken equal to 26 in the case of the sub- 

 merged rod of rectangular section, in Fig. 62. A, 

 its lower half is identical to that of the floating 

 rectangular box in the same figure, which has a 

 draft of a and a beam of 2a. For 2a = 26 of the 

 first case the added liquid mass m/, for the up- 

 and-down motion is 1.51p7ra^; for the second case 

 it is 0.767rpa^. 



It is rare that any surface ship, except possibly 

 an old canal boat or a special barge, has a con- 

 stant transverse section, or one that could be 

 termed average for the entire length. Manifestly, 

 the shape of the actual transverse sections, and the 

 distribution of this shape along the ship length, 

 determine the flow pattern at different stations, 

 the kinetic energy in the surrounding unsteady 

 flow, and the added mass of the liquid. Further, 

 the boat, barge, or ship has a finite length, with 



Unit Lenqth Between — »^ — »^ 

 Planes Normal to Axis 



Mode of TrbnslQtionol 

 Periodic Motion in the 

 Vertical Plane 



Sinalc Amplitude 



Surroundinq Liouid is Assumed 

 to be Ideal and Liquid Motion 

 is Entirely Two-DimensionQl 



Mode of Motion of Ends 



All Seqments Are of Circular Section 

 of Radius a^ 



Ellipsoid of Revolution in Midposition 



-Lenqth of One Seqment 



Ends Down. Hoc^aina 



In Both Cases, Two-Dimensionol Flow 



is Assumed to Take Place About Each 



Seament Independently, Between the 



tporollel Planes Indicated, Normal to 



the Midposition Axes 



--Midposition Axis 



In Dioqratns Z and 3 

 Deformation is by Pure Shear 



Fig. 62.E First Stage in Transformation of Oscillating Cylindrical Bar to Ship Structure in 2-Nodbd 



Vertical Vibration 



