Continuity Equation & Fluid Dynamics – AP Physics 2 | ShowMeClass

🌊

Continuity Equation & Flow Rate

AP Physics 2 · Unit 1: Fluids

Learning Objectives

State the equation of continuity: A₁v₁ = A₂v₂

Explain why fluid speeds up in narrower sections

Calculate volume flow rate Q = Av

Relate continuity to conservation of mass

Key Equations

Visual Guide

Wide section (slow flow)

Narrow section (fast flow)

Fluid particles

Velocity vectors

Intuition

Think of a garden hose: pinch the end and water sprays faster. The same volume of fluid must pass through every cross-section per unit time. Smaller area → higher velocity. This is conservation of mass for incompressible fluids.

ContinuityFlow RateFluidsAP Physics 2

Q =—

v₁ =—

v₂ =—

v₂/v₁ =—

VELOCITY & AREA ALONG PIPE

Wide Area A₁ (cm²) 20

Narrow Area A₂ (cm²) 5

Input Velocity v₁ (m/s) 2.0

Particle Count 30

Pipe Shape

Display

Continuity Analysis

📝 Quick Quiz▼

1. The continuity equation A₁v₁ = A₂v₂ assumes the fluid is:

Compressible Incompressible Viscous Turbulent

2. If the cross-section halves, the velocity:

Halves Doubles Stays the same Quadruples

3. Volume flow rate Q has SI units of:

m/s m²/s m³/s kg/s