This paper deals with both the axial and the tangential annular flows of power-law fluids in concentric annuli, and it specifically focuses on the relation volumetric flow rateQagainst pressure dropP. Initially the mutual compatibility of the hitherto obtained results is analyzed, and from this, new results concerning behavior of a parameter λ [a location of maximum axial (tangential) velocity component] are derived. Then, approximative expressions for relationsQagainstP(independent of A.) are proposed in a sufficiently large region (K,n) where K represents annular aspect ratio andnthe flow behavior indexn. The deviations of these simple relations from the exact ones are negligible.