These equations must be solved by numerical approximations for an actual glacier, but they may be solved exactly for idealized glaciers of many shapes; this has been done for eight idealized examples. The results show that the velocity of flow is usually greatest near the annual firn limit and very small near the head and the terminus.
The theory predicts longitudinal expansion in the accumulation area and longitudinal contraction in the ablation area. Transverse surface profiles of equilibrium glaciers are generally higher in the center than at the edges in the ablation area, but in the accumulation area the transverse profiles are generally dish-shaped.
Large rates of ablation require large velocities of flow in order to maintain equilibrium. This concept is used to explain some of the phenomena often observed near ice-dammed lakes.