AAMC FL Practice Exam

Which equation represents Bernoulli's principle?

1. P1 + 1/2pv^2 + pgh1 = P2 + 1/2pv2^2 + pgh2

2. P1 + v + h = P2 + v + h

3. v = Q/A

4. P = 8nL/Q

The correct answer is: P1 + 1/2pv^2 + pgh1 = P2 + 1/2pv2^2 + pgh2

Bernoulli's principle is fundamentally about the conservation of energy in a fluid flow, encapsulating the relationship between pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume. The correct equation representing Bernoulli's principle articulates that the total mechanical energy along a streamline remains constant. In the equation, each term represents a different form of energy per unit volume: the first term is the static pressure (P), the second term is the dynamic pressure related to fluid velocity (1/2pv^2), and the third term is the hydrostatic pressure due to elevation (pgh). The equation equates the total energy at one point in the fluid (the left side) with the total energy at another point (the right side), effectively capturing the essence of energy conservation within the fluid system. Other options do not conform to Bernoulli's principle. One of them mixes different variables unrelated to fluid dynamics, while another describes a different relationship not pertaining to energy conservation in a fluid context. The remaining choice references Poiseuille's law in fluid mechanics rather than Bernoulli's equation. All these distinctions highlight why the selected equation is the appropriate representation of Bernoulli's principle.