1. Clicker Question Room Frequency BA FB mplasticg
A solid piece of plastic of volume V, and density ρplastic is floating partially submerged in a cup of water. (The density of water is ρwater.) What is the buoyant force on the plastic?
A) Zero
B) ρplastic V
C) ρwater V
D) ρwater V g
E) ρplastic V g FB
mplasticg
The plastic is in equilibrium so FB = mplasticg = ρplastic V g !

2. Announcements CAPA assignment #13 is due on Friday at 10 pm.
This week in Section: Assignment #6
Start reading Chapter 11 on Vibrations and Waves
I will have regular office hours 1:45 – 3:45 in the Physics Helproom today

3. Fluids in Motion: Fluid Dynamics
Many, many different types of motion depending on particular properties of fluid: waves, rivers, geysers, tornados, hurricanes, ocean currents, trade winds, whirlpools, eddies, tsunamis, earthquakes, and on and on!
We’ll focus on the simplest motion: flow

4. Fluids in Motion: Flow Two main types of flow: Laminar and Turbulent
We’ll focus on the simplest flow: laminar flow

5. Analysis of Flow Use conservation laws!
Analyzing flow at the force level is mathematically complex 
Use conservation laws!
1) Conservation of Mass: the Continuity Equation
2) Conservation of Energy: Bernoulli’s Equation

6. Continuity Equation
Consider the flow of a fluid through a pipe in which the cross sectional area changes from A1 to A2
The mass of fluid going in has to equal the mass of fluid coming out: conservation of mass!
The speed of the fluids must be different!

7. Continuity Equation
To analyze this mass conservation, we calculate the mass flow rate:
Flow rate in =
must equal
Flow rate out =

8. Mass Flow Rates
Flow rate in =
Flow rate out =
Continuity Equation:

9. Continuity for Incompressible Fluids
If the fluid is incompressible: ρ1 = ρ2 so
Does this make sense?

10. Clicker Question Room Frequency BA
“Incompressible” blood flows out of the heart via the aorta at a speed vaorta. The radius of the aorta raorta = 1.2 cm. What is the speed of the blood in a connecting artery whose radius is 0.6 cm?
vaorta
2 vaorta
(2)1/2 vaorta
4 vaorta
8 vaorta

11. Bernoulli’s Equation: Conservation of Energy
Earlier in the course we learned:
Applied to fluid flow, we consider energy of pieces of fluid of mass Δm

12. Bernoulli’s Equation: Incompressible Fluids
Now using
and the continuity equation you get
Bernoulli’s Equation:

13. Applications of Bernoulli’s Equation
Bernoulli’s Equation is behind many common phenomena!
Curve balls
Aerodynamic Lift
Sailing into the wind
Transient Ischemic Attacks (“mini-strokes”)
Light objects getting sucked out your car window
Shower curtains bowing in
Flat roofs flying off houses in Boulder!
Ping pong ball demo

14. Flat Roof Example
Wind flows over a flat roof with area A = 240 m2 at a speed of voutside = 35 m/s (125 km/h = 80 mi/h). What net force does the wind apply to the roof?
Inside Outside hh
v = 35 m/s h

15. Clicker Question Room Frequency BA
For an airplane wing (an air-foil) the upward lift force is derivable from Bernoulli’s equation. How does the air speed over the wing compare to the air speed under the wing? It is……
Faster
Slower
Same
Unknown
F = lift=(Pbot-Ptop)(Wing Area)
faster
slower
On the top side, the air has to travel farther to meet at the back edge of the wing!

16. Oscillations!
Throughout nature things are bound together by forces which allow things to oscillate back and forth.
It is important to get a deeper understanding of these phenomena!
We’ll focus on the most common and the most simple oscillation: Simple Harmonic Motion (SHM)
Requirements for SHM:
There is a restoring force proportional to the displacement from equilibrium
The range of the motion (amplitude) is independent of the frequency
The position, velocity, and acceleration are all sinusoidal (harmonic) in time

17. Mass and Spring

18. A Simple Harmonic Oscillator: Spring and Mass!
Note:
restoring force is proportional to displacement
force is not constant, so acceleration isn’t either: a = -(k/m)x
“amplitude” A is the maximum displacement xmax, occurs with v = 0
mass oscillates between x = A & x = -A
maximum speed vmax occurs when displacement x = 0
a “cycle” is the full extent of motion as shown
the time to complete one cycle is the “period” T
frequency is the number of cycles per second: f = 1/T (units Hz)