Final answer:
Fluid velocity is greatest where streamlines are closest together due to the conservation of mass, which requires fluid velocity to increase when the cross-sectional area decreases in order to maintain the mass flow rate. The correct answer is b) Streamlines represent flow rate.
Step-by-step explanation:
In physics, especially in the study of fluid dynamics, fluid velocity is a key concept. When examining streamlines in fluid flow, we notice that the fluid velocity is greatest where the streamlines are closest together. This is due to conservation of mass, also known as the principle of continuity.
The conservation of mass dictates that the mass flow rate must remain constant from one cross-section to another. For an incompressible fluid, this means the product of the cross-sectional area and the velocity must remain constant.
If the cross-sectional area through which a fluid flows becomes smaller, the fluid must speed up to maintain the same mass flow rate. Thus, where streamlines converge and the cross-sectional area decreases, the fluid velocity must increase. This behavior is often shown in diagrammatic representations of fluids moving through various shapes of pipes or around objects.
According to the conservation of mass, the flow rate (volume of fluid passing through a point per unit time) must remain constant within an incompressible fluid.
Therefore, to maintain the constant flow rate, the fluid must flow faster where the streamlines are closer together, resulting in a higher fluid velocity.