The correct answer is: D. the fluid particles move in plane or parallel planes and the streamline patterns are identical in each plane.
A true one-dimensional flow is a flow in which the velocity of the fluid particles is constant in both magnitude and direction. This means that the fluid particles move in a straight line and do not change direction or speed.
Option A is incorrect because the direction and magnitude of the velocity do not have to be identical at all points. For example, in a laminar flow, the velocity of the fluid particles is highest near the center of the pipe and decreases towards the walls.
Option B is incorrect because the velocity of successive fluid particles does not have to be the same at successive periods of time. For example, in a turbulent flow, the velocity of the fluid particles is constantly changing.
Option C is incorrect because the magnitude and direction of the velocity can change from point to point in the fluid. For example, in a converging flow, the velocity of the fluid particles increases as they move towards the center of the pipe.
Option D is the correct answer because it describes a flow in which the fluid particles move in plane or parallel planes and the streamline patterns are identical in each plane. This type of flow is often found in pipes and ducts.