932 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. X4.6 



definite values whether they are dimensional or 

 dimensionless. When the concepts forming parts 

 of dimensional parameters are given certain 

 accepted values it is then possible to express their 

 relationships to the dimensionless values, for any 

 given system of measurement. There are tabu- 

 lated in this section certain ratios which occur 

 frequently in the treatment of hydrodynamic 

 problems in ship design. 



One such ratio in everyday use is that between 

 the Taylor quotient T^ and the Froude number 

 F„ . By definition and accepted practice, T^ = 

 Y I ■\/L, where V is in kt and L in ft; by consistent 

 units, F„ = V/'s/^L, where V is in ft per sec, 

 g in ft per sec", and L in ft. The ratio between 

 Ta and F„ depends upon the "standard" value 

 assumed for the acceleration of gravity g and 

 the length of a nautical mile. At a latitude of 

 45 deg and at sea level, g is taken as 32.174 ft per 

 sec''. For this book, 1 nautical mile is 6080.20 ft. 

 Then 



^ F (ft per sec) ^ 1.6889F(kt) 

 \/gL V32.174L (ft) 



= 0.2978 -^y^ = 0.2978r, 



0.2978 



= 3.358F„ 



0.3T„ and 



quently used in hydrodynamic ship-design prob- 

 lems, together with their frequently used powers 

 and with logarithms of these numbers to the 

 base 10, are listed hereunder in a form to make 

 them readily available for calculation purposes. 

 For certain special numbers the grouping is 

 in accordance with the general subjects discussed 

 in Parts 1 and 2. 



For rule-of-thumb work, F„ 

 T^ = 10i^„/3. 



Corresponding values of the pair T, and F„ , 

 and the pair F„ and T, are listed in Table X4.c, 

 for a range sufficient to cover all design problems 

 for boats and ships, small and large. 



Another conversion that needs to be made 

 often is the one between D. W. Taylor's dis- 

 placement-length quotient A/(0.010L)^ and the 

 0-diml fatness ratio F/(0.10L)^ A conversion 

 factor has to be fixed here because of Taylor's 

 use of a specific gravity for salt water of 1.024, 

 corresponding to a volume of 35.075 ft^ per long 

 ton. For converting from the displacement-length 

 quotient to the 0-diml fatness ratio, the former is 

 multiplied by 0.035075 or divided by 28.510. To 

 obtain values of the displacement-length quotient 

 from the 0-diml fatness ratio, multiply the latter 

 by 28.510 or divide it by 0.035075. 



Table X4.d lists corresponding values of these 

 two quantities. 



X4.6 Frequently Used Numbers, Their 

 Powers, and Logarithms. The numbers fre- 



LENGTHS AND AREAS 

 12, 



144, 



1,728, 



3.281 ft per meter. 



logio = 1.07918 



log.o = 2.15836 



logio = 3.23754 



logio = 0.51601 



SPEEDS AND VELOCITIES 



1.6889 ft per sec for Ikt, in 

 this book, logio = 0.22760 



1.467 ft per sec for 1 mph, logio = 0.16643 



1.6878 ft per sec for inter- 

 national knot, 1954, 



1 



1. 



= 0.5921, 



(1.6889)' = 2.8524, 



ACCELERATIONS 

 g = 32.174 ft per sec' 



•\/32.174 = 5.6722, 

 1 



logio = 0.22732 

 logio = 9.77240 

 logio = 0.45521 



logio = 1.50751 

 logio = 0.75375 



\/32.174 



= 0.17630, logio = 9.24625 



KINEMATIC VISCOSITY 



When Knu) = 1.2285(10"'), then 

 1 



= 0.8140(10') 



When V 



1.2285(10"') 

 = 1.2817(10"'), then 

 1 



1.2817(10"') 

 WAVE ACTION 



= 0.7802(10') 



6.2832 

 V2^ = 2.50663 

 1 



= 2.2629 English units 



= 1 .2493 metric units 



V2^ 



= 0.39894. 



