Both of them only and merely say that the inflows around a point equal to the outflows from that point. What is the difference then?
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1$\begingroup$ They are two completely different things. What do you mean by differ? $\endgroup$– YashasCommented Jul 18, 2017 at 12:19
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$\begingroup$ For a hydraulics network, for instance, they state the same thing. $\endgroup$– matlabcrzCommented Jul 18, 2017 at 12:22
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$\begingroup$ The Kirchhoff's law is for electric currents & conservation of mass is for mass. The Kirchhoff's law talks about the flow of charges but flow of mass does not make much sense without context. $\endgroup$– YashasCommented Jul 18, 2017 at 12:24
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1$\begingroup$ They are analogous concepts. They obviously don't state the exact same thing; but you can interpret them in the same way. $\endgroup$– JMacCommented Jul 18, 2017 at 12:32
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1$\begingroup$ I'm really not sure what you expect to get as an answer to this beyond what was already said. You can model hydraulic circuits as electrical circuits (for some conditions) and therefore can solve some problems using the same techniques. The differences are simple. One is for fluids, the other is for electricity. $\endgroup$– JMacCommented Jul 18, 2017 at 13:13
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1 Answer
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The Kirchoff Current Law can be stated as: $$ I=\int_{s}\mathbf{i}\cdot \mathbf{ds}=0 $$
While the Mass Conservation can be stated as: $$ Q=\int_{s}\mathbf{q}\cdot \mathbf{ds}=0 $$
In both cases, the integral, which is normally expressed as a simple sum, equals the total flux of current|caudal outside a certain closed control surface called "node". In this regard, both laws are equivalent under the given variable.
Note that a rotational current|caudal tangential to the surface $s$ will leads to no flux, hence the vectorial dot calculation is required.
Also note, that both "laws" are particular cases. As you clearly can note, these expressions must be corrected in order to include accumulation of charge|mass $q$|$m$, such in a capacitor|tank, introducing a time derivative of the total charge|mass inside the control surface.
