The invention provides a fluid analysis apparatus, a method for operating a fluid analysis apparatus, and a fluid analysis program that display a flow velocity vector such that the tendency of a fluid flow is easily checked. A representative two-dimensional flow velocity vector representing a plurality of two-dimensional flow velocity vectors obtained by projecting three-dimensional flow velocity vectors of a plurality of voxels that overlap each other in a projection direction of a projection plane to the projection plane is acquired from three-dimensional volume data that has information of the three-dimensional flow velocity vector indicating the flow velocity of a fluid in an anatomical structure for each voxel and is displayed.
