Practical Application Of The Principles Of Conservation And Continuity

In practice, the principle of conservation of salt is most often used, together with the principle of continuity, to study the flow, or the evaporation-precipitation balance, of relatively enclosed bodies of water with limited connections with the main ocean. These might be fjords, estuaries, or semi-enclosed seas like the Mediterranean or the Baltic.

Figure 6.12 represents a channel, or some other semi-enclosed body of water, bounded by two vertical transverse sections with areas A, and A2. Water enters the channel through A, at a rate of V, m3 s_l and leaves it through A2 at a rate of V2 m3 s"1. Between A, and A2, water also enters the channel as a result of precipitation and run-off, and is removed by evaporation. The net rate at which water is being added by these processes is represented by F, which is also measured as volume per unit time (m3 s-' ). If we assume that the volume of water in the portion of channel under consideration remains constant over a given period of time (and that water is incompressible), we may equate the total volume of water entering this portion of the channel with the total volume leaving, i.e.

Figure 6.12 Ttie flaw ot water into and out of a length of channel Wafer flows into the channel through the section with ares ^ at a rate ol l^i m3 s and oul through the section with area 4? at a rate of K. m3 s_1.

Figure 6.12 Ttie flaw ot water into and out of a length of channel Wafer flows into the channel through the section with ares ^ at a rate ol l^i m3 s and oul through the section with area 4? at a rate of K. m3 s_1. II we fu it her assume that the average salinity between the sections remains constant, the amount of salt entering through A t must equal thai leaving through A:. because the processes of precipitation, run-off and evaporation do nol involve any net transfer of salt, Bccause satiruly values are ef fectively parts per thousand by weight I although salinity has no units -see Figure 6 11 caption), ihe mass of salt in a kilogram of sea water is the density (in kg nr1) times the salinity. Thus, the mass of salt transported across A, and A2 per second must be V^pjSj and VipiSi. and these must be equal to one another, i.e.

where ph p?. and.?,. Si are. respectively, the mean densities and salinities of the water at A \ and A*- Proportional changes in density are very small compared with those of salinity - lor example, a change in salinity from 30 to 3b (i.e. over almost the complete range of salinities found in the oceans) results in an increase in density of less lhan 0.5^. We may therefore ignore changes in density and write:

We now have two equations that we may solve for either l7, or V2. From Equation 6.3:

Hence, substituting for V, in Equation 6.2: