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 control closed 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.

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.

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 flow of current / caudal outside a certain control surface called "node". In this regard, both laws are equivalent under the given variable.

Note that a rotational current/caudal will leads to no flow, hence the vectorial dot flow calculation is required.

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 control closed 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.