922 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. X3.7 



TABLE X3.1 — Data on Change of State op Fresh and Salt Water 

 The data on vapor pressure of fresh water are taken from H. Rouse [EMF, 1946, Table XI, p. 364]. The note concerning 

 the vapor pressure of sea water is taken from page 67 of the book "The Oceans: Their Physics, Chemistry, and General 

 Biology," by H. U. Sverdrup, M. W. Johnson, and R. H. Fleming, 1942. Table 29 on page 116 of the reference, not 

 reproduced here, lists the "maximum vapor tension in millibars" over water of 3.5 per cent salinity for a range of tem- 

 perature from —2 deg C to 32 deg C. 



presence of other solutions is to lower it slightly. 



The freezing point of salt water having a 

 salinity of about 35 parts per thousand, corre- 

 sponding to 3.5 per cent, is from —1.9 deg C to 

 perhaps —3 deg C; probably it is close to —2 

 deg C. The last figure corresponds to about 

 28.5 deg F. 



X3.7 Elastic Characteristics of Water and 

 Other Common Liquids. The bulk modulus of 

 elasticity of a liquid, also called the volume 

 modulus of compressibility, represented by the 

 symbol K, is defined as the ratio of the change in 

 pressure to the volumetric strain [Binder, R. C, 

 "Fluid Mechanics," 1947, p. 160], or as "the ratio 

 of a differential unit compressive stress to the 

 relative reduction in volume which the stress 

 produces" [Rouse, H., EMF, 1946, p. 328]. 

 Expressed in symbols. 



K 



Ap 

 AV 

 V 



Ap 



' av 



V 



The value of K in English engineering units is of 

 the order of 300,000 psi. 



According to H. Rouse [EMF, 1946, p. 363] the 

 values of the bulk modulus K given in Table 

 X3.m, which apply to its elastic characteristics 

 at atmospheric pressure, increase by about 2 per 

 cent for each 1,000 lb per sq in rise in pressure 



intensity. H. U. Sverdrup, M. W. Johnson, and 

 R. H. Fleming, on page 69 of the reference cited 

 in the two preceding sections, indicate a reduc- 

 tion in mean compressibility, in bars, of from 

 4,659 at deg C, at the surface, to 4,009 at about 

 10,000 meters, or a depth of over 32,000 ft. The 

 values listed in Table X3.m for salt water are 

 based upon a 9 per cent increase in elastic modulus 

 under average conditions [Rouse, H., EMF, 1946, 

 p. 363]. 



The speed of sound c in any medium is the 

 square root of the quotient of the bulk modulus 

 of elasticity K and the mass density p. In symbols 

 it is c = 'vK/p. For salt water at 5 9 deg F, 

 15 deg C, this is V'339,000(144)/1.9905 = 4,954 

 ft per sec, approx. 



The following is quoted from page 363 of the 

 Rouse reference: 



"If the nominal value of E (the symbol K ia used here) 

 for fresh water is taken as 300,000 pounds per square inch, 

 corresponding values for other common Uquids will be as 

 follows: 



Salt water, 330,000 (This is a 10 per cent increase) 



Glycerme, 630,000 



Mercury, 3,800,000 



Oil 180,000 to 270,000 pounds per square inch." 



X3.8 Mechanical Properties of Air and Ex- 

 haust Gases at Atmospheric Pressure and at Sea 

 Level. There appear to be some slight variations 



