1 Class #6 of 30 Homework #2 – “HAP” Rocket with gravity Retarding forces Projectile motions with viscous drag Plausibility of Newton’s Law Projectile motions with inertial drag Homework #3 – CM of a sphere Demo – High Speed photography :15

2 Falling raindrops I Problems: A small raindrop falls through a cloud. At time t=0 its velocity v=0. Describe it’s velocity vs. time. Raindrop is 10  m diameter, density is 1 g/cc, viscosity of air is 180  Poise z x :18

3 Falling raindrops II 1) Newton 2) On z-axis 3) Rewrite in terms of v 4) Variable substitution 5) Solve by inspection z x :23

4 Falling raindrops III 1) Our solution 2) Substitute original variable 3) Apply boundary conditions 4) Expand “b” 5) Define v terminal :30

5 Inertial Drag I Plate with area “ A n ” moves a distance through fluid with density The mass of the fluid displaced is Mass “M” must acquire a velocity “v” to move out of the way of the plate. The moving plate is causing Rearranging we get AnAn :35

6 Inertial Drag II – A sphere  Previously demonstrated  “A n ” means “A normal to velocity”  Form factor for sphere  Plug ‘n’ play :40

7 Falling raindrops redux Problems: A small raindrop falls through a cloud. At time t=0 its velocity is zero. Describe it’s velocity vs. time. Raindrop is 1000  m diameter, density is 1 g/cc. z x

8 Falling raindrops redux II 1) Newton 2) On z-axis 3) Rewrite in terms of v 4) Rearrange terms 5) Separate variables z x :45

9 Falling raindrops redux III :50

10 Tanh and sinh and cosh, oh my :55

11 L6-1 Liquid water drops on Io A small water droplet is traveling sideways on a cloud on Jupiter’s moon Io. At time t=0 its velocity is purely horizontal Io is tiny. Neglect gravity. Draw forces on the droplet. Write down differential equation for velocity assuming Stokes-law force. Solve to get raindrop’s velocity vs. time. Calculate the “decay time” for droplet velocity assuming R=100 um and  for Io’s atmosphere =20  -poise. :60

12 Falling raindrops L6-2 A small raindrop falls through a cloud. It has a 1000  m radius. The density of water is 1 g/cc. The viscosity of air is 180  Poise. The density of air is 1.3 g/liter at STP. a) Draw the free-body diagram. b) What should be the terminal velocity of the raindrop, using quadratic drag? c) What should be the terminal velocity of the raindrop, using linear drag? d) Which of the previous of two answers should we use?? e) What is the Reynolds number of this raindrop? :70

13 Integration in Different Coordinates :45

14 Lecture #6 Wind-up. Read sections Matlab Basics :72  Linear Drag  Quadratic Drag