AAMC FL Practice Exam

What element of fluid dynamics does the equation A1V1 = A2V2 represent?

1. Conservation of energy

2. Resistance

3. Continuity of flow

4. Fluid pressure

The correct answer is: Continuity of flow

The equation A1V1 = A2V2 represents the principle of continuity in fluid dynamics, which is known as the continuity of flow. This principle states that for an incompressible fluid flowing through a pipe or a channel, the mass flow rate must remain constant from one cross-section of the pipe to another. Here, A1 and A2 represent the cross-sectional areas of the fluid at two different points, while V1 and V2 represent the fluid velocities at those corresponding points. When the area of the pipe decreases (A2 < A1), the fluid must flow faster (V2 > V1) to ensure that the same amount of fluid passes through both sections in the same amount of time, thereby conserving mass. This relationship highlights how changes in cross-sectional area result in changes in fluid velocity, demonstrating the consistency of flow in a fluid system. Other concepts, such as the conservation of energy, resistance, and fluid pressure, while relevant to fluid dynamics, do not specifically encapsulate the relationship described by this equation. The continuity equation directly relates to how the flow remains constant within a fluid system, emphasizing the importance of cross-sectional areas and fluid velocity.