Physics 2 · Unit 1: Fluids · 14 min read · Updated 2026-05-11
Fluid Dynamics — AP Physics 2
AP Physics 2 · Unit 1: Fluids · 14 min read
1. Fundamentals of Fluid Dynamics★★☆☆☆⏱ 3 min
Fluid dynamics is the branch of fluid mechanics focused on fluids (liquids and gases) in motion, in contrast to fluid statics which studies stationary fluids. For AP Physics 2, this topic accounts for approximately 1–2% of your total exam score, as part of Unit 1 which contributes 10–14% of total weight. It appears in both multiple-choice and free-response sections, often paired with other energy or force concepts to test multi-step reasoning.
All analysis in AP Physics 2 is restricted to ideal incompressible fluids with non-viscous, steady (laminar) flow, the standard approximation for all exam problems unless explicitly stated otherwise.
2. Continuity Equation and Volume Flow Rate★★☆☆☆⏱ 4 min
For incompressible fluids, density $\rho$ is constant, so conservation of mass requires that the mass of fluid entering a pipe segment equals the mass exiting. The density term cancels out, leaving the continuity equation:
A_1 v_1 = A_2 v_2 = Q = \text{constant}
The core intuition is that flow speed increases when the pipe narrows, which matches everyday experience: placing your thumb over the end of a garden hose reduces cross-sectional area, increasing flow speed to make water spray farther.
3. Bernoulli's Equation★★★☆☆⏱ 5 min
Bernoulli's equation is derived from conservation of mechanical energy for ideal fluid flow along a streamline (the path a single fluid particle follows through the flow). It relates three terms: pressure (work done on the fluid per unit volume), kinetic energy per unit volume, and gravitational potential energy per unit volume. For any two points along the same streamline, the sum of these terms is constant:
P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2
The key takeaway, called the Bernoulli effect, is that for flow at the same height, an increase in flow speed corresponds to a decrease in pressure. This effect explains airplane wing lift and the curve of a spinning soccer ball. If flow speed is constant along the flow path, Bernoulli's equation reduces to the static pressure relation you already learned for stationary fluids.
4. Torricelli's Law of Efflux★★★☆☆⏱ 4 min
Torricelli's law is a special case of Bernoulli's equation that describes the speed of fluid flowing out of a small hole in an open tank. Two key simplifications apply for this configuration: (1) both the tank surface and the hole are open to the atmosphere, so pressure terms cancel; (2) the cross-sectional area of the tank is much larger than the area of the hole, so the speed of the dropping fluid surface $v_1 \approx 0$.
If we let $h = h_1 - h_2$ be the height difference between the fluid surface and the hole, substituting into Bernoulli's equation gives Torricelli's law:
v = \sqrt{2 g h}
This result matches the speed of a solid object dropped freely from height $h$, which makes sense because gravitational potential energy from the fluid column converts directly to kinetic energy of the exiting fluid.
5. AP-Style Concept Check★★★★☆⏱ 6 min
Common Pitfalls
Why: Students get in the habit of using gauge pressure after seeing atmospheric pressure cancel in Torricelli's law problems, and forget consistency when only one side is open to atmosphere
Why: Students substitute diameter directly into the equation instead of accounting for area being proportional to diameter squared
Why: Students assume the constant energy sum applies to any two points in the fluid, even when they are not on the same flow path
Why: Students memorize Torricelli's law and use it regardless of the relative size of the hole and tank
Why: AP problems almost always assume ideal flow, so students forget Bernoulli ignores energy loss from friction