Sec. 40.6 



BASIC CONCEPTS FOR CALCULATIONS 



Force L = (1)(0.5) 



L'f 



niL 



The last expression has the dimensions of a force. 



40.6 The Derivation and Use of "Specific" 

 Terms. The term "specific" as now applied to 

 ship resistances of various kinds is not a new term 

 to marine architects by any means but it has 

 come into extended use only during recent years. 

 It will surely be encountered more frequently in 

 the years to come. The term expresses, in 0-diml 

 numbers or as a ratio, the relationship between 

 some quantity under consideration and a quantity 

 having the same characteristics which is taken 

 as a standard or reference. 



The best-known use of this term is in the 

 expression specific gravity, as applied to a liquid. 

 Here the specific gravity of any liquid is repre- 

 sented by the 0-diml ratio of (1) the weight of 

 unit volume of liquid to (2) the weight of unit 

 volume of standard fresh water. In this case, 

 fresh water is taken as a reference because it is 

 readily available, widely used, and its weight per 

 unit volume is easily determined. 



Another familiar but unfortunate term is the 

 one known as specific weight; unfortunate because 

 it is not truly dimensionless. It signifies the weight 

 of a substance per unit volume and is expressed 

 by the symbol w. While it does have a reference 

 basis of sorts, it has nevertheless the dimensions 

 of a weight divided by a volume. Broken down 

 into its dimensional elements, explained in 

 Appendix 2, and with a weight given the dimen- 

 sions of a force, w = Force/L^ = {mL/f)/L^ = 

 m/{LH-). 



Practically all the customary specific resistance 

 terms now employed in naval architecture and 

 marine engineering are dimensionless. An example 

 is the specific pressure coefficient, often called 

 simply the pressure coefficient. This expresses 

 the ratio between (1) a pressure difference Ap (or 

 an absolute pressure) at a given point on a body 

 and (2) the ram pressure q developed at the 

 forward stagnation point of that body at the 

 relative speed U. In the form Ap/(0.5pC/^) the 

 pressure coefficient is also known as the Euler 

 number E^ . In the form (p„ — e)/(0.5pf7^), where 

 e is the vapor pressure of the liquid, it is the 

 cavitation number o-(sigma). 

 ^ Another example is the specific drag coefficient 

 Cd , or simply the drag coefficient. This expresses. 



in simple numerical form, the ratio of (1) the 

 drag force on a given body, moving at a relative 

 speed U, at a certain attitude and under given 

 conditions in a liquid, to (2) the force that would 

 be exerted on the body if the ram pressure 

 q (or 0.5pU^) acted uniformly over its entire 

 projected area A. Here 



^ ^ Drag 



Still another familiar specific resistance coeflGicient 

 is that for friction resistance, expressed by Cf ■ 

 This 0-diml coefficient is again the ratio of (1) the 

 friction resistance Rp to (2) a ram-pressure force, 

 but the reference area in this case is the wetted 

 surface S of the body rather than its projected 

 area. Hence 



Rf 



Cf = 



SU' 



Provided the flows around two bodies are in 

 all respects dynamically similar, and the bodies 

 are geosims (geometrically similar), it is possible 

 to determine from model tests and to tabulate for 

 ready reference the drag coefficients of objects 

 having many different forms and running at 

 various attitudes, as in Fig. 55. B. The tests 

 may be made, furthermore, in any convenient 

 medium by using the proper mass-density value 

 in the specific-coefficient formula. Similarly, the 

 coefficients apply to motion in any other medium. 



When devising, calculating, and using specific- 

 resistance terms, it is most important that the 

 reference length, area, or volume be carefully 

 understood and defined. For example, in the 

 expression for the lift coefficient of a hydrofoil or 

 a rudder, Cl = L/(0.5pAU^), the area A is that 

 of the projected or lift-producing area. In other 

 words, it is the area of the planform or the lateral 

 area of the blade bounded by the profile, as 

 projected on the plane of the base chords. In the 

 expression for hydrofoil drag coefficient, Cd = 

 D/{0.5pAU^), the area A usually remains the 

 projected area as before, notwithstanding that 

 this area is projected on a plane Ijdng generally 

 at right angles to the direction in which the drag 

 force is exerted. In the expression for the specific 

 friction-resistance coefficient of either rudder or 

 hydrofoil, where tangential forces are involved, 

 Cf = Rf/(0.5pSU^). Here S is the superficial or 

 wetted area of both sides of the rudder blade or 

 hydrofoil. 



