AP Physics 1 (Part 32: Fluid Dynamics) | Office Hours with Al

This session was used to cover a few topics involving fluids in motion. We discussed flow rate and the equation of continuity, Bernoulli's Principle, and applications such as lift and down force. The rest of our time was spent covering example problems for these topics.

See the course plan here:

|Chapters|
0:00 Plans for the Day
4:34 Homework Problems from Last Time
30:01 Revisiting Pascal's Principle
41:50 Two More Properties of Ideal Fluids
47:15 Flow Rate and the Continuity Equation
1:07:20 Bernoulli's Principle and Bernoulli's Equation
1:32:59 Torricelli's Theorem
1:41:55 Applications to Bernoulli's Principle (Lift, Down Force, Pitot Tubes, Atomizers, and Keels)
2:09:59 Example: Mass Flow Rate of Blood in an Aorta
2:17:49 Example: A Liquid Flowing into a Narrower Pipe
2:29:52 Example: Inhaling Air
2:32:06 Example: Water Spilling from a Tank
2:48:58 FAILED Example: Finding the Diameter of the Constriction in a Venturi Tube
3:08:53 Example: Drawing Liquid with a Siphon
3:21:45 Final Comments

[althetutor]

Some corrections and clarifications:

1. For the problem starting at 2:32:06, the diameter of the hole was unnecessary information, so I was worried about it for nothing.

2. For the problem starting at 2:48:58, I was overthinking it. The radius of each section doesn't need to be taken into account when determining the depth because we only need the *external* pressure difference, which can be calculated just from the height difference of the static fluid in the columns that sits above the moving fluid in the tubes. My Bernoulli equation for the problem should've been this:

P₁ + ½ρv₁² = P₂ + ½ρv₂²
(P₀ + ρgd₁) + ½ρv₁² = (P₀ + ρgd₂) + ½ρv₂²
ρgd₁ + ½ρv₁² = ρgd₂ + ½ρv₂²
gd₁ + ½v₁² = gd₂ + ½v₂²

From there, you'd use 10 cm (= 0.1 m) for d₁ and 5 cm (= 0.05 m) for d₂, which leaves you with the two unknowns v₁ and v₂. I calculated v₁ in the video, so you can substitute its value to get v₂, then use v₂ in the continuity equation to solve for A₂, then finally use A₂ with the area formula for a circle to find that the diameter of the narrow section is about 0.0147 m, or 1.47 cm.