50 The Sea-water and its Physical and Chemical Properties 



can be derived, where jj. is the cubic compressibiHty. For sea-water where Oq = 28 

 (34-84%o S) at temperatures of 0" and 30°C respectively, /3 = 15 x 10^« and 334 x 

 10-« grad-i and ix = 46-59 x IQ-^^ and 42-07 x lO-^^ jyn-i cm^. From this it can be 

 found that k -= 1-0004 and 1-0207 for 0°C and 30°C respectively. At greater depths ^J. 

 is smaller and there k is larger than at the surface. 



(h) The thermal conductivity coefficient A is defined by the equation 



Q = -x(ddidx), 



where Q (cal/sec) is the amount of heat passing through 1 cm- at right angles to the 

 flow and dd ( C) is the change in temperature along a distance d.x (cm) in the direction 

 of flow. A thus has the dimensions (cal cm~^ sec~^ grad"^). For pure water A = 

 0-001325 + 4 X 10-«/. 



A has not been determined directly for sea-water; as a first approximation, according 

 to Weber's rule, the ratio of the thermal conductivities of two substances is the same 

 as that of the thermal capacities of equal volumes. This gives the values shown in 

 Table 16 for the coefficient of thermal conductivity for different salinities. 



Table 16. Coefficient of thermal conductivity at different salinities 



Salinity (%„) 



10 I 20 



30 I 35 40 



Thermal conductivity I ! 



coefficient (X 10-») 1-400 1-367 1-353 • 1-346 ! 1-341 1-337 



For oceanic water (35%o S) the thermal conductivity coefficient is about 4-2% less 

 than for pure water. The temperature conductivity coefficient is the quantity a = XJipCp) 

 and has the dimensions (cm- sec~^). For sea-water pCj, is not very different from 1 and 

 the numerical difference between A and a is slight. 



(c) In fluids with motion there is a shear stress between every layer in the direction 

 of flow and the adjacent parallel layer, and this shearing stress is proportional to the 

 velocity gradient perpendicular to the direction of flow, that is 



dv 

 ^ dz 



The proportionality factor /x is a measure of viscosity or inner (molecular) friction 

 (g cm~^ sec~^). For many flow phenomena there occurs the coefficient i- = /x/p, 

 the kinematic viscosity (cm- sec "^). These frictional coefficients decrease rapidly 

 with increasing temperature. For pure water, the values shown in Table 17 are ob- 

 tained. According to the investigations of Krummel and Ruppin (1905) viscosity 

 increases very little with salinity; at 0°C by 3-9 or 5-2% for 25%o S and 35%o S re- 

 spectively and at 30X' by 6- 1 or 8-2"o. The effect of pressure appears to be negligible. 



Table 17. Viscosity coefficients for pure water 

 (g cm"i sec"^) 



Temperature ( C) 10 j 20 30 40 



/x 0-0179 0-0131 , 0-0100 1 00080 00065 



