A dimensionless formulation of the acceleration terms of the Saint-Ven
ant equations is presented for one-dimensional overland flows under ei
ther laminar or turbulent conditions. For stationary storms over a pla
ne surface of uniform roughness, dimensionless analytical expressions
are derived during the rising limb for the local acceleration a(l), a
nd during equilibrium for the convective acceleration a(c) and the pr
essure gradient a(p) ((13), (14), and (15), respectively). In terms o
f the order of magnitude, the three acceleration terms are inversely p
roportional to the kinematic flow number K. At equilibrium, the pressu
re gradient a(p) is also inversely proportional to the square of the
Froude number Fr. The relative magnitude of the acceleration terms for
supercritical overland flow (a(l) > a(c)* > a(p)*) differs from subc
ritical overland flow (a(p) > a(l)* > a(c)*), which in all cases cont
rasts with open-channel flows (a(p) > a(c)* > a(l)*). The kinematic w
ave approximation is therefore only suitable when both K and Fr are la
rge. Improvements using the diffusive wave approximation are only poss
ible for subcritical overland flow. Both the diffusive wave and the qu
asi-steady dynamic wave approximations are not suitable for supercriti
cal overland flow. The analysis of moving storms corroborates these fi
ndings in that the local acceleration exceeds the convective accelerat
ion. These effects are particularly pronounced during the rising limb
of overland flow hydrographs for downstream moving rainstorms.