  A simulation of the hydrodynamics on the two dimensional non-commutative
space is performed, in which the space coordinates $(x, y)$ are
non-commutative, satisfying the commutation relation $[x, y]=i \theta$. The
Navier-Stokes equation has an extra force term which reflects the
non-commutativity of the space, being proportional to $\theta^2$. This
parameter $\theta$ is related to the minimum size of fluid particles which is
implied by the uncertainty principle, $\Delta x \Delta y \ge \theta/2$. To see
the effect of this parameter on the flow, following situation is considered. An
obstacle placed in the middle of the stream, separates the flow into small slit
and large slit, but the flow is joined afterwards in the down stream. For the
Reynolds number 700, the behavior of the flows with and without $\theta$ is
observed to differ, and the difference is seen to be correlated to the
difference of the activity of vortices in the down stream. The oscillation of
the flow rate at the small slit diminishes after the certain time in the usual
flow when the "two attached eddies" appear. In the non-commutative flow this
two attached eddies appear from the beginning and the behavior of the flows
does not fluctuate largely. The irregularity in the flow existing in the
beginning disappears after the certain time.
