AAMC FL Practice Exam

What principle does the continuity equation a1v1 = a2v2 represent?

1. Conservation of mass

2. Conservation of energy

3. Conservation of momentum

4. Conservation of charge

The correct answer is: Conservation of mass

The continuity equation \( a_1v_1 = a_2v_2 \) embodies the principle of conservation of mass in fluid dynamics. This equation 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 flow to another. In this equation, \( a \) represents the cross-sectional area of the flow at different points, and \( v \) denotes the fluid velocity at those points. As a fluid moves through a pipe with varying diameters, when the cross-sectional area decreases, the velocity of the fluid must increase to maintain a constant mass flow rate. Conversely, if the area increases, the velocity decreases. This relationship ensures that the mass of the fluid entering a section of the pipe is equal to the mass of fluid exiting that section, demonstrating that mass is conserved as the fluid flows through the system. The other principles listed do not relate directly to this equation: conservation of energy pertains to the total energy within a system, conservation of momentum deals with the motion of objects in response to forces, and conservation of charge involves the principle that electric charge must be conserved in an isolated system. Thus, the continuity equation specifically exemplifies the conservation of