Final answer:
The velocity of water flow in a stream is fastest near the center due to less friction and resistance compared to the bed and the walls. Streamlines being closest together indicate higher fluid velocities due to smaller cross-sectional areas, as seen in stream dynamics during conditions like spring runoff.
Step-by-step explanation:
The velocity of water flow in a stream is not constant throughout the stream. It tends to be fastest near the stream's center rather than along the bed of the stream or the walls of the stream's channel. This is because the water in the center of the stream experiences less friction than the water that is in contact with the bed and the walls of the stream channel. The resistance between the water layers and the friction with the shore or stream bed creates a velocity profile where the speed is greatest at the center and decreases toward the edges due to the no-slip condition, where the velocity at the wall is effectively zero.
Fluid velocity is greatest where streamlines are closest together because this indicates that the fluid is moving through a smaller cross-sectional area, and according to the principle of conservation of mass for incompressible fluids, the velocity must increase if the cross-sectional area decreases (assuming a constant flow rate). This is often seen in mountain streams where, during high flow conditions like spring runoff, the flow velocity increases as the water's path narrows due to obstructions or changes in channel geometry.
Fluid dynamics and the distribution of velocities within a stream can be complex due to factors such as viscosity, turbulence, and the presence of obstructions that can cause resistance and alter flow patterns. Nonetheless, these principles are consistent with observations of fluid behavior in nature and within engineered channels.