Fluid flow apparatus, such as a fluid flow meter, a fluid mixing device or a fluid dispersing device, includes a fluid displacement member (40) mounted in a conduit (20) and having a sloped exterior wall (48) forming a periphery on the member for deflecting the fluid to flow through a region of progressively decreasing area defined between the periphery of the member and the interior surface of the conduit. The displacement member is a hollow frustum (42) terminating at the plane of its outer peripheral edge (46) and accommodating flow measurements at or adjacent the axis of the conduit at or adjacent the plane of the peripheral edge of the displacement member.