  In recent years, open systems with balanced loss and gain, that are invariant
under the combined parity and time-reversal ($\mathcal{PT}$) operations, have
been studied via asymmetries of their solutions. They represent systems as
diverse as coupled optical waveguides and electrical or mechanical oscillators.
We numerically investigate the asymmetries of incompressible viscous flow in
two and three dimensions with "balanced" inflow-outflow
($\mathcal{PT}$-symmetric) configurations. By introducing
configuration-dependent classes of asymmetry functions in velocity, kinetic
energy density, and vorticity fields, we find that the flow asymmetries exhibit
power-law scaling with a single exponent in the laminar regime with the
Reynolds number ranging over four decades. We show that such single-exponent
scaling is expected for small Reynolds numbers, although its robustness at
large values of Reynolds numbers is unexpected. Our results imply that
$\mathcal{PT}$-symmetric inflow-outflow configurations provide a hitherto
unexplored avenue to tune flow properties.
