Abstract: Under the circumstances of sport space area being full of medium and sport space area being full of medium and vacuum, we propose two computing methods about the rate of change over time of volume integral that divergence of vector field to a sports region of space. If a special viewpiont look upon the change of integraition space area is used, the two kinds of circumstances could be computed by the use of a unified way. Under the circumstances of sports space region being full of medium and vacuum, if the velocity v is keeped to be the same as the one on the boundary face S of the integration V conform to the truth, but give V a new veloctiy field v（r,t） which rate of change with the space is continuous or block continuous, the computing method of locking volume ele- ment is still applicable.

Key words: divergence of vector field, sports region of space, volume integral, volume element, the rate ofchang over time, shrict theory