Freshwater and a well-mixed salt inventory
For a well-mixed reservoir with solution mass M,positive salt fraction s and conserved salt mass Ms, freshwater gain/loss gives ds/dt=−(s/M)dM/dt.
Key knowledge
For a well-mixed reservoir with solution mass M,positive salt fraction s and conserved salt mass Ms, freshwater gain/loss gives ds/dt=−(s/M)dM/dt. This follows from d(Ms)/dt=0. Rainfall dilutes and salt-free evaporation concentrates the reservoir; seawater exchange or salt-bearing input requires a separate salt flux rather than this closed-salt formula.
Values and equations
d(Ms)/dt=0; ds/dt=−(s/M)dM/dt
- M
- changing reservoir solution mass kg
- s
- uniform salt mass fraction kg kg⁻¹
- t
- time s
Conditions and scope
- M>0,uniform mixing,unchanged salt inventory and negligible salt in the stated incoming/outgoing freshwater. Track varyingM explicitly.
- Evaporation is not a chemical removal of dissolved salts. Ice, brine, rainfall chemistry and inflow/outflow can change the salt inventory; a fixed-depth virtual-salt-flux convention must be named rather than confused with the physical mass-changing reservoir.
Sources · 1
References
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Evidence and review
Derived exactly by differentiating the salt inventory under explicit freshwater-only boundary assumptions, using inspected mass/salt conservation. No claim of an exact fixed-ocean-volume mass budget or an empirical seawater salinity formula.
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Entry details
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