AAMC FL Practice Exam

In the context of fluid dynamics, what does the continuity principle state?

1. A1 + V1 = A2 + V2

2. A1V1 = A2V2

3. A1/V1 = A2/V2

4. A1/V1 = A2 - V2

The correct answer is: A1V1 = A2V2

The continuity principle, often referred to as the principle of conservation of mass in fluid dynamics, asserts that the mass flow rate must remain constant from one cross-section of a pipe or a flow system to another, provided no fluid is added or lost between those sections. This principle is mathematically expressed as the product of the cross-sectional area (A) and the fluid velocity (V) at two different points in the system being equal. In the context of the continuity equation, the equation A1V1 = A2V2 demonstrates that the product of the area and velocity at one point (1) is equal to the product of the area and velocity at another point (2). This means that if the area decreases (the fluid flows into a narrower section of the pipe), the velocity must increase to keep the product constant, and vice versa. Understanding this principle is crucial in analyzing how fluids behave in various situations, such as in pipelines, around wings of aircraft, or through nozzles. The other options do not accurately reflect the conservation of mass in fluid flow, making the correct understanding of the continuity principle vital for solving problems related to fluid motion.