The invention provides a fluid analysis apparatus, a method for operating a fluid analysis apparatus, and a fluid analysis program that perform display such that the tendency of a fluid flow in a blood vessel is easily checked. Route position information that is capable of identifying an order along a route of the anatomical structure is assigned to each position in the anatomical structure, using three-dimensional volume data in which each voxel has the information of a three-dimensional flow velocity vector indicating a flow velocity of a fluid in an anatomical structure. The three-dimensional flow velocity vector is selected such that the route position information of a position where the three-dimensional flow velocity vector is present is sequentially arranged from one point in the anatomical structure and a trajectory indicating the flow of the fluid is drawn so as to be visibly recognized.
