Sec. 62 J 



ESTIMATE OF ADDED LIQUID MASS 



435 



of constant rectangular section having a beam B 

 (26 in his paper) , a draft H of half the beam, and 

 a unit length. Its body mass ma is therefore 

 p(5)(B/2)(1.0) = pBV2 per unit length; in 

 Koch's notation it is 2pb^. Therefore, to obtain 

 the added mass mi, of entrained liquid for a 

 buoyant rectangular-section body of beam B, 

 applying to any given combination of the variables 

 listed in the second paragraph preceding, it is 

 necessary to multiply Koch's "added mass factor" 

 by pB' 12. Then for the given rectangular- 

 section body of beam B, the added-liquid mass 

 JWi, = <^pB'/2 per unit length. 



The reference body of Prohaska is a buoyant 

 one of semicircular section having a flat, hori- 

 zontal top and a curved under side, with a 

 beam B {2b in the paper), a draft H of half the 

 beam (6 in the paper), and a unit length. Its 

 body mass m^ is therefore p(7r/8)-B^ per unit 

 length; in Prohaska's notation it is 0.5xpt>^. 

 Hence, to obtain the added mass wii for a floating 

 body having a beam B and any type of constant 

 section within the limits of Prohaska's tests, 

 depicted in his Fig. 19, and for any combination 

 of the variables listed by Prohaska (section 

 coefficient /3 and depth-draft ratio T/d), it is 

 necessary to multiply his "coefiBcient" C by 

 0.125xpB^. Thus for the given body of beam B, 



the added liquid mass m/, = C(0.125)7rpB" per 

 unit length. 



The reference body of Prohaska has a semi- 

 circular section which can be inscribed within the 

 rectangular section of Koch. Therefore, it has a 

 mass vib which is x/4 times that of Koch, from 

 which it follows that Prohaska's C = 4<t>/Tr or 

 Koch's ^ = xC/4. 



The data of C. W. Prohaska, set down in (2) 

 preceding, were obtained with 2-diml (constant- 

 section) models of limited length and of varied 

 section shape and fullness, moved bodily up and 

 down in a tank of water, with their longitudinal 

 axes parallel to the water surface. The water 

 depth h was varied by altering the position of an 

 adjustable bottom. It was found that V-type 

 transverse sections always gave greater added- 

 mass coefficients than U-type sections, and that 

 the wii-values for hollow sections were approxi- 

 mately the same as for sections which had the 

 hollows filled out by drawing tangents between' 

 tlie projecting points. 



Fig. 62. L, adapted from one of the several 

 shallow-water graphs given by Prohaska, namely 

 Fig. 32 on page 204 of the 1947 ATMA paper, 

 summarizes in diagram 1 the shape-factor or 

 Prohaska "coefficient" C data in terms of (1) 

 the section coefficient, based on the local beam 



3 4 5 



F?atio of Water Depth h to Draft H 



Via. 62. L Added-Liquid-Mass Data op C. W. Prohaska for a Surface Ship With Normal Sections, Vibrating 



Vertically in Shallow Water 



