AP Physics 1 Fluids: Dynamics, Flow, and Conservation Principles

Fluid

A material that can flow and take the shape of its container (in AP Physics 1, usually modeled as a liquid and often treated as incompressible).

Incompressible (fluid assumption)

An idealization where the fluid’s density is constant, so volume flow rate is conserved in steady flow.

Pressure

Force per unit area exerted by a fluid on a surface; relates force and area by P = F/A.

Pressure force

The contact force a fluid exerts on a surface due to pressure; it acts perpendicular (normal) to the surface and has magnitude F = PA.

Net force from a pressure difference

If pressures on two sides of the same area A differ, the net force is F_net = (P1 − P2)A, directed from higher pressure to lower pressure.

Pressure gradient (concept)

A change in pressure across space that produces a net pressure force on a fluid element, causing acceleration (needed for speed changes in flow).

Newton’s Second Law in fluid contexts

The idea that once fluid pushes are written as forces (often via pressure differences), you can apply ΣF = ma to a fluid element or object.

Newton’s Third Law in fluids

If a fluid exerts a force on a wall/container, the wall exerts an equal and opposite force on the fluid (action–reaction pair).

Thrust (fluid-related root idea)

A forward force on an object that results when fluid is pushed backward; boundaries exert forces on fluid to redirect/accelerate it, and the fluid pushes back equally and oppositely.

Fluid element

A tiny “blob” of fluid imagined to move with the flow, used to analyze forces such as pressure forces, weight, and (if not neglected) viscous forces.

Viscosity

Internal friction in a real fluid that causes energy dissipation; neglected in the “nonviscous” ideal-fluid model.

Ideal fluid (AP Physics 1 approximation)

A model assuming the fluid is incompressible, nonviscous, and in steady flow—conditions under which Bernoulli’s equation applies.

Steady flow

A flow condition where properties at a given point (like speed and pressure) do not change with time.

Continuity equation (incompressible form)

Conservation of mass for steady incompressible flow: A1v1 = A2v2.

Volume flow rate (Q)

Volume per time passing through a cross-section; Q = Av.

Mass flow rate (m-dot)

Mass per time passing through a cross-section; ṁ = ρAv.

Density (ρ)

Mass per unit volume of a fluid; ρ = m/V (often taken constant for liquids in AP Physics 1 problems).

Bernoulli’s equation

Energy conservation along a streamline for steady, incompressible, nonviscous flow: P + (1/2)ρv^2 + ρgy = constant.

Streamline

A path in the flow used for Bernoulli analysis; Bernoulli is applied between two points along the same streamline in ideal conditions.

Pressure energy per unit volume (Bernoulli term)

The P term in Bernoulli’s equation, representing the ability of pressure forces to do work on the fluid per unit volume.

Kinetic energy per unit volume (Bernoulli term)

The (1/2)ρv^2 term in Bernoulli’s equation, representing kinetic energy density of the moving fluid.

Gravitational potential energy per unit volume (Bernoulli term)

The ρgy term in Bernoulli’s equation, representing gravitational potential energy density due to elevation y.

Venturi-style pressure drop

In a narrowing (often horizontal) pipe, continuity can increase speed and Bernoulli predicts a lower pressure in the faster-flowing narrow section.

Torricelli’s law

Efflux speed from a small hole a height h below a tank’s free surface (both at atmospheric pressure): v = √(2gh), assuming surface speed is negligible.

Gauge vs. absolute pressure (exam pitfall)

Two ways to reference pressure (relative to atmosphere vs. including atmosphere); for forces from pressure differences, you must compare pressures consistently (what matters is ΔP).