A set of equations averaged over a well-defined cylindrical plasma layer is derived. A new snowplow equation, which is based on energy conservation, is derived from the set and is examined. This equation gives descriptions for the later phase of a pinch and differs from the 'snowplow' equation which is based on momentum conservation. It is shown that the plasma collapses to a smaller radius in a Z-pinch when the initial imploding velocity increases. A Z-pinch can be enhanced by superposing a pre-current, which gives similar initial conditions.