  The uncertainty relations in hydrodynamics are numerically studied. We first
give a review for the formulation of the generalized uncertainty relations in
the stochastic variational method (SVM), following the paper by two of the
present authors [Phys. Lett. A382, 1472 (2018)]. In this approach, the origin
of the finite minimum value of uncertainty is attributed to the
non-differentiable (virtual) trajectory of a quantum particle and then both of
the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are
reproduced. The same non-differentiable trajectory is applied to the motion of
fluid elements in hydrodynamics. By introducing the standard deviations of
position and momentum for fluid elements, the uncertainty relations in
hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii
equation and then the field-theoretical uncertainty relation is reproduced. We
further investigate numerically the derived relations and find that the
behaviors of the uncertainty relations for liquid and gas are qualitatively
different. This suggests that the uncertainty relations in hydrodynamics are
used as a criterion to classify liquid and gas in fluid.
