518 Currents in a Strait 



solely antitryptic, that is, the pressure and the frictional forces will be in equilibrium 

 see p. 323). The system will be subject to the equations 



1 dp 

 Y - Ri = 0= 1 and 3) along 1 and 3 (XVI.3) 



and 



1 dp 

 g ^ - Ri = (/ = 2 and 4) along 2 and 4, 



where i?, is the effect of friction along each of the sections. Multiplying the equations 

 (XVI.3) by p and integrating along the individual sections one obtains, after adding, 

 the relations: 



g( \dz-\-\pciz~(()pR,ds] = 0, (XVI.4) 



\ Jb Jd J abed I 



g{P2 - PA)h = (b pRi ds. (XVI.5) 



J abed 



Here pg ^^id p^ are the mean densities in the vertical water columns 2 and 4. All the 

 quantities Ri are positive and depend on the current velocity. From (XVI.5) it follows 

 then that the left-hand side must also be positive. That is, the mean density in be 

 must be greater than in ab or p, > Pi- This relation thus fixes the direction of the 

 current in the strait and also give the dependence of the current velocity on the 

 density distribution in the water masses. This can be used to find an approximate 

 value for the current velocity maintained by the thermodynamic forces acting inside 

 the system. According to the circulation theorem, when a = Xjp 



- i adp = i Rids XVI.6) 



J abed J abed 



and since Z), 



p 



a dp 







gives the dynamic depth of the pressure surface p in the water column /, we obtain 

 from (XVI.6) 



D,- D, = (/?! + i?3)/ + (^2 + ^4)/^. (XVI.7) 



The integral — j adp is the work done by the pressure forces in the system ; if it is 

 positive, this work can thus be balanced by the work required by the friction. The 

 relation (XVI.6) states that, in the thermodynamic machine the expansion takes place 

 at a higher pressure than the contraction. Since an expansion is associated with an 

 input of heat and a contraction is associated with a heat loss, the heat gain must 

 therefore occur at a higher pressure than the heat loss. Actually, in the model of 

 the sea strait in point there will be a higher pressure and a higher temperature, the 

 latter due to a greater heat gain. Such a sea strait system is thus a true thermodynamic 

 machine in action. 



The current intensities in a strait can be calculated approximately by means of the 

 above equation (XVI.5). For a channel of length /, if friction is neglected in the vertical 

 part of the circulation, the equation will take the form 



2pR/ = g{p, - p,)h. (XVI.8) 



