Conservation of Energy in Fluid Flow — AP Physics 2
AP Physics 2 · AP Physics 2 CED Unit 1: Fluids · 14 min read
1. Core Concept: Energy Conservation for Fluid Flow★★☆☆☆⏱ 3 min
Conservation of energy in fluid flow adapts the work-energy theorem to moving fluid, forming the foundation of Bernoulli's principle, a high-frequency topic on the AP Physics 2 exam. It accounts for work done by pressure forces on continuous moving fluid parcels, leading to an extra pressure term in the energy balance. All terms in the resulting equation are measured as energy per unit volume of fluid, simplifying calculations for continuous flow.
2. Bernoulli's Equation: Derivation and Core Terms★★★☆☆⏱ 5 min
Bernoulli's equation is the mathematical statement of conservation of energy for fluid flow. To derive it, we apply the work-energy theorem to a fluid parcel moving between two points (1 and 2) along a streamline.
P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2
Exam tip: Always confirm your two points lie along the same streamline before applying Bernoulli's equation — AP problems frequently test the assumption that the energy constant is only identical along a single streamline, not across the entire fluid.
3. Torricelli's Law: Efflux Speed from a Container★★★☆☆⏱ 3 min
Torricelli's law is a common special case of Bernoulli's equation that describes the speed of fluid draining out of a small hole in a large open container.
Exam tip: If the problem gives you the container opening area explicitly, do not assume $v_1 = 0$. Use continuity to relate $v_1$ and $v_2$, then substitute into the full Bernoulli equation — AP problems often test this trick where the container is not infinitely large.
4. Applications: Venturi Effect and Airfoil Lift★★★★☆⏱ 3 min
Combining the continuity equation and Bernoulli's equation gives many practical results that are frequently tested on the AP Physics 2 exam. The **Venturi effect** states that when fluid flows through a constricted (narrower) section of pipe, flow speed increases per continuity, so static pressure decreases per Bernoulli. This effect is used in Venturi flow meters and carburetors.
A second common AP application is **airfoil lift**: air flowing over the curved upper surface of an airfoil moves faster than air under the flat lower surface, leading to lower pressure on the top of the airfoil and a net upward lift force.
Exam tip: When explaining lift on an FRQ, you must explicitly link higher speed to lower pressure (via Bernoulli) then to the net upward force from the pressure difference — omitting the force step will cost you points.
Common Pitfalls
Why: Students memorize the approximation but don't check if it is justified by the problem geometry.
Why: Students forget the derivation is for flow along a single streamline.
Why: Students often use 0 gauge pressure for points open to atmosphere but absolute pressure for the other point.
Why: Students forget the core assumptions of the derivation.
Why: Students rush to plug in values before simplifying based on geometry.