Physics of How Things WorkFluid in Motion

Chapter 6

Vortex Cannon

Vortex Cannon

Which way does it travel?

Why?

Vortex Cannon

Which way does it travel?

Why?

Which way does it spin?

Why?

Vortex Cannon

Which way does it travel?

Why?

Which way does it spin?

Why? flow rate ∝ 1viscosity

Vortex Cannon

Vortex Cannon

When does it stop and why?

Mr. Bernoulli

As speed increases, pressure decreases

Mr. Bernoulli

As speed increases, pressure decreases

P1 + ρgh1 +12ρv1

2 = P2 + ρgh2 +12ρv2

2

Mr. Poiseuille

ΔVΔt

= π ⋅ΔP ⋅D4

128 ⋅L ⋅η

Flow Rate = π ⋅Pressure difference ⋅Diameter4

128 ⋅Length ⋅viscocity

Example #1

How fast will honey flow through a straw that is 5” (0.127m) long (it has a diameter of 10 mm) if you have perfect lung power.

Example #2

A 68 cm tall Gatorade tank is full up to the lid which also allows air inside. How fast does the gatorade flow out of the tap when the tap is opened?

Example #3

Airplanes

Lift

Weight

DragThrust

3 axis of flight

Pitch Axis Roll Axis Yaw Axis

3 axis of flight

3 Control surfaces

Flaps

Slats

Lift vs. drag

Laminar Flow

Turbulent Flow

Causes of Turbulent Flow

Viscosity of fluid

Speed of fluid

Obstacle size

Fluid density

Reynolds number

Reynolds number = fluid density ⋅obstacle width ⋅ fluid speed

viscosity

Turbulence happens when the Reynolds number exceeds 2300

viscous dominated vs. inertia dominated

Example

How fast can a small (~ 2 cm wide) fish swim before it looses control?

What about ball sports?

Curve BAll

1.Thrower gives the ball a forward speed and puts a spin on the ball

Curve BAll

2.The spin causes one side of the ball to have a higher relative air speed. Which side has the higher speed?

V

v

Curve BAll

3.Because of the higher air speed on the right side, the Reynold’s number exceeds 2300 on that side alone!

V

v

reynolds number = fluid density ⋅obstacle width ⋅ fluid speed

viscosity

Curve BAll4.Because the Reynold’s number was so high on the right

side, turbulence occurs on the right side of the ball (but not the left)

Curve BAll5.Because turbulence occurs on the right side of the ball,

the air does not stick to the ball on that side

Curve BAll

6.Because of the low relative air-speed on the left side of the ball, the air sticks to the ball (through friction).

v

Curve BAll

7.As the ball continues to rotate, it pulls the air on the left side to the right.

Curve BAll

8.Ball pulls air to the right. Therefore,air pulls the ball to the left

This is called the “Magnus Force”

Curve BAll9.The constant push to the left coupled with the

forward motion causes the ball to curve left.

Curve

Spin, turbulence, & strikes

motionSpin

Curve

Why do golf balls have dimples?

Why do golf balls have dimples?

Why do golf balls have dimples?

Why do golf balls have dimples?

Quick Quiz

A vortex from a vortex cannon rotates

A.Clockwise (as viewed from the shooter)

B.Counterclockwise (as viewed from the shooter

C.doesn’t rotateD.From the middle forward

and then backwards on the outer edge

Quick Quiz

Why do umbrella’s flip up in a gust of wind?

A.Because of Bernoulli’s Principle

B.Because of Pascal’s Principle

C.Because of Poiseuille’s Principle

D.Because of Reynolds’ Principle

Quick Quiz

In order for an airplane to comfortably turn, which control surfaces must be used?

A.ElevatorB.SlatsC.FlapsD.AileronsE.Rudder