Physics 1 · Unit 8: Fluids and Thermal Physics · 14 min read · Updated 2026-05-11
Bernoulli's Principle — AP Physics 1
AP Physics 1 · Unit 8: Fluids and Thermal Physics · 14 min read
1. Core Concept of Bernoulli's Principle★☆☆☆☆⏱ 3 min
Bernoulli's principle is derived directly from conservation of mechanical energy applied to moving fluid systems. For AP Physics 1, this topic makes up ~1-2% of the total exam score, appearing in both multiple-choice and short free-response questions. Notation used in this guide matches standard AP exam conventions.
2. The Continuity Equation (Conservation of Mass)★★☆☆☆⏱ 4 min
Before applying Bernoulli's principle to most AP problems, you first need the continuity equation, which comes from conservation of mass for incompressible steady flow. For flow through a closed pipe, mass entering per unit time equals mass leaving, so for constant density, volume flow rate is constant.
Q = A_1 v_1 = A_2 v_2
For circular pipes, $A = \pi d^2/4$, so the constant terms cancel when taking the ratio of areas, giving the simplified relation $d_1^2 v_1 = d_2^2 v_2$, which saves significant time on AP exams.
Exam tip: Always check intuition: if the pipe narrows, output speed must be higher than input. If you get a lower speed, you flipped the diameter ratio.
3. Bernoulli's Equation (Quantitative Principle)★★★☆☆⏱ 5 min
Bernoulli's equation is the quantitative expression of the principle, representing conservation of mechanical energy per unit volume of fluid. For any two points along a streamline in valid flow, the sum of pressure energy, kinetic energy, and gravitational potential energy per unit volume 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
Each term has units of pressure (Pa, equivalent to J/m³). The key conceptual takeaway for same height ($h_1 = h_2$) is that an increase in flow speed always corresponds to a decrease in pressure, and vice versa. AP Physics 1 expects you to remember default values: $\rho_{\text{water}} = 1000$ kg/m³ and $P_{atm} = 1.01 \times 10^5$ Pa.
Exam tip: When working with gauge pressure, you can ignore atmospheric pressure entirely if both points are open to the atmosphere, since it cancels out and simplifies arithmetic.
4. Torricelli's Law (Special Case for Tank Drainage)★★★☆☆⏱ 4 min
One of the most common AP applications of Bernoulli's principle is Torricelli's Law, which describes the exit speed of fluid from a small hole in a large open tank. Two key approximations apply here: 1) the tank area is much larger than the hole area, so the surface speed is negligible ($v_{\text{surface}} \approx 0$), and 2) both the surface and hole are open to the atmosphere, so pressures are equal.
Exam tip: On conceptual FRQs, always state the two key approximations (negligible surface speed, equal atmospheric pressure) to earn full credit.
5. Common AP Applications★★★★☆⏱ 5 min
Bernoulli's principle explains many common real-world phenomena tested on AP Physics 1, including airplane lift, which arises from pressure difference between the top and bottom of the wing.
Common Pitfalls
Why: Students forget the inverse relationship between area and speed, mixing up which area corresponds to which speed.
Why: Problems often give gauge pressure, and students forget all pressure terms must use the same reference frame.
Why: Students get used to horizontal pipe problems and forget to check for height differences between points.
Why: Students memorize the 'higher speed = lower pressure' rule and forget it only applies when points are at the same height.
Why: Students forget the continuity approximation that surface speed is negligible for large tanks, leading to incorrectly low exit speed.