  An exact formulation of two dimensional chiral hydrodynamics with
diffeomorphism and conformal anomalies is provided. The constitutive relation
involving the stress tensor is computed. It reveals a one parameter class of
solutions which is a new result. For a particular value of this parameter, the
results found in the gradient expansion scheme are reproduced. Moreover, the
constitutive relation is analogous to the corresponding relation for an ideal
fluid, appropriately modified to include the chirality property, which has also
been derived here.
