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AP Physics 1 Unit 8: Fluid Dynamics & Bernoulli

Topics 8.3–8.4 (New for 2025, 10–15% exam weight): Static fluids → moving fluids. Master Continuity (mass conservation) and Bernoulli (energy conservation) for pipe flow, airplane lift, and leaking tanks.

1. Continuity Equation (Mass Conservation)

Incompressible fluids: **same volume flow rate** throughout pipe. Narrow pipe → faster flow.

$A_1 v_1 = A_2 v_2$

Area × Velocity = Constant | Diameter ×2 → Area ×4 → Velocity ÷4

Garden hose thumb test: smaller opening = faster water.

Hose Test: Cover half nozzle → water shoots twice as far.

2. Bernoulli’s Equation (Energy Conservation)

Total “fluid energy” stays constant. Trade-offs between pressure, height, and speed.

$P + \rho g h + \frac{1}{2}\rho v^2 = \text{CONSTANT}$

**Key Insight:** Fast fluid = LOW pressure (airplane lift!)

⚠️ Bernoulli Trap: Fast air = LOW pressure. Hurricane roofs fly OFF (low P outside, high P inside pushes up). Slow misconception loses points.

3. Torricelli’s Theorem (Leaking Tanks)

Hole in tank → exit speed from Bernoulli (P₁=P₂=atmospheric, neglect small height difference).

$v = \sqrt{2 g h}$

Exit speed = free-fall speed from height h above hole

Tank Hole: Deeper hole = faster leak (like dropped rock).

4. Quick AP Practice

📚 AP Practice Problems

1. Pipe diameter halves. Flow speed?

Answer

**4x faster.** A∝r², diameter÷2 → A÷4 → v×4 (A₁v₁=A₂v₂).

2. Airplane wing: air faster top or bottom?

Answer

**Top (faster).** Longer path → higher v → lower P → lift.

3. Tank hole 5m below surface. Exit speed?

Answer

v=√(2×10×5)=√100=**10 m/s**.

🔗 Unit 8 Navigation

🎉 AP PHYSICS 1 UNIT 8 COMPLETE!

You finished Fluids! From Kinematics to Bernoulli, your AP Physics 1 curriculum is now 100% mastered.

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