DDEEVVIILL PPHHYYSSIICCSS INTRO VIDEO

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Relaxing Ocean Waves

Lesson 10.7:

Fluids In Motion;

Flow Rate and the Equation of Continuity

1. Fluid Dynamics – study of fluids in motion

2. Hydrodynamics – study of water in motion

3. Streamline or laminar flow – flow is smooth,

neighboring layers of fluid slide by each other

smoothly, each particle of the fluid follows a smooth

path and the paths do not cross over one another

4. Turbulent flow – characterized by erratic, small

whirlpool-like circles called eddy currents or eddies

a) Eddies absorb a great deal energy through

internal friction

5. Viscosity – measure of the internal friction in a flow

6. Speed changes in changing diameter of tubes

a) Assuming laminar flow

b) Flow rate – the mass (Δm) of fluid that passes

through a given point per unit time (Δt)

c) The volume of fluid passing that point in time

(Δt) is the cross-sectional area of the pipe (A)

times the distance (Δl) travelled over the time

(Δt)

d) The velocity is equal to the distance divided by

the time,

m = ρV

e) Since pressure is constant throughout a fluid,

the flowrate will remain constant even if the

diameter of the pipe changes:

This is called the equation of continuity.

f) If the fluid is incompressible, then ρ1 = ρ2 and

The units for this are m3/s which represents a

volume rate of flow

g) This tells us that when the cross-sectional area

of the pipe is large, the velocity is small. But

when the cross-sectional area is small, the

velocity is high.

h) That’s why you put your thumb over the end of

the hose to squirt kids far away at car washes.

7. EXAMPLE: Blood Flow. The radius of the aorta is

about 1.0cm and the blood passing through it has a

speed of about 30cm/s. A typical capillary has a

radius of about 4x10-4

cm and blood flows through it

at a speed of about 5x10-4

m/s. Estimate how many

capillaries there are in the body.

A1 = area of aorta = πr12

A2 = area of all capillaries in the body = N πr22

(N = number of capillaries)

or 3.75 billion capillaries

Note: For all the Bioweenies not taking Physics next

year, if you need help filling out your worksheets you

can always stop by DDEEVVIILL PPHHYYSSIICCSS for help.

Lesson 10.8:

Bernoulli’s Equation

1. Daniel Bernoulli (1700-1782) is the only reason

airplanes can fly.

2. Ever wonder why:

a) The shower curtain keeps creeping toward you?

b) Smoke goes up a chimney and not in your

house?

c) When you see a guy driving with a piece of

plastic covering a broken car window, that the

plastic is always bulging out?

d) Why a punctured aorta will squirt blood up to

75 feet, but yet waste products can flow into the

blood stream at the capillaries against the

blood’s pressure?

e) How in the world Roberto Carlos made the

impossible goal?

f) It’s Bernoulli’s fault

3. Bernoulli’s principle states, where the velocity of a

fluid is high, the pressure is low, and where the

velocity is low, the pressure is high.

4. Not as straight forward as it sounds. Consider this:

a) We just said that , which means

that as the fluid flows from left to right, the

velocity of the fluid increases as the area gets

smaller

b) You would think the pressure would increase in

the smaller area, but it doesn’t, it gets smaller.

c) But, the pressure in area 1 does get larger.

Blowing Paper DEMO

5. When you wash a car, your thumb cramps up

holding it over the end of the hose.

a) This is because of the pressure built up behind

your thumb.

b) If you were to stick your pinky inside the hose,

you would feel pressure at the tip of your finger,

a decrease in the pressure along the sides of

your finger, and an increase in the velocity of

the water coming out of the hose.

c) You would also get squirted in the face but

that’s your own fault for sticking your finger in

a hose!

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Bernoulli's Principle

6. Bernoulli’s Equation:

a) Assumptions:

i) Flow is steady and laminar

ii) Fluid is incompressible

iii) Viscosity is small enough to be ignored

b) Fluid is flowing through a pipe like the one

below

SPLIT SCREEN

c) We want to move the blue fluid in (a) to the

position shown in (b)

i) On the left, the fluid must move a distance

of Δl1

ii) Since the right side of the tube is narrower,

the fluid must move farther (Δl2) in order to

move the same volume that is in Δl1

d) Work must be done to move the fluid and we

have pressure available to do it

e) The work done on the right side is found the

same way:

The negative sign is because the force exerted

on the fluid is opposite to the motion (i.e., the

fluid on the left does work on the fluid on the

right)

f) There is also work done by gravity (since the

pipe has an increase in elevation) which acts on

the entire body of fluid that you are trying to

move. The force of gravity is mg, work is force

times distance, so work for this problem is:

g) The sum of our labors:

h) The equation is still not large enough, so,

according to the work-energy principle, work

done on a system is equal to the change in

kinetic energy:

i) However, since m has a volume of A1Δl1 = A2Δl2,

we can substitute m = ρA1Δl1 = ρA2Δl2 and then

divide everything by A1Δl1 = A2Δl2:

j) To pretty it up, let’s put all the parts for the left

half of the pipe on the left, and the right stuff on

the right:

TaDaah! This is Bernoulli’s Equation!

7. What is the impact of this principle on the human

circulatory system?

a) At the capillaries, where all the important

exchanges take place, the velocity is high, but

the pressure is low – perfect environment for all

of those exchanges to take place.

Lesson 10.9:

Applications of Bernoulli’s Principle:

From Torricelli to Sailboats, Airfoils and TIA

8. Torricelli’s Theorem – a special case of Bernoulli’s

Principle.

a) Consider the flow of water from a water tower

(point 2) to a spigot in a house (point 1).

b) Both ends are open to the atmosphere so P1=P2

and they can be subtracted from the equation.

c) Assuming that the diameter of the pipe at the

tower is much larger than that of the spigot, the

velocity of the water at the tower approaches

zero in comparison and is disregarded.

d) The equation then becomes:

OR

9. Another special case of Bernoulli: fluid flow

without appreciable change in height:

This is the form of the equation we are most

accustomed to using to explain many fluid

phenomena:

b) It also explains Roberto Carlos’ impossible

goal:

http://www.youtube.com/watch?v=dwRYYeEk5

Eg&NR=1

Bernoulli makes impossible goal possible

Per 3, 5/24, Stopped Here

c) Bernoulli’s equation can also be used to explain

medical phenomena such as transient ischemic

attacks (TIA), a temporary lack of blood supply

to the brain.

DEMO

Look Ahead Video

Homework

Problems #34-41, 43

Optional Reading

University Physics, Page 432-434

Holt Physics, Page 274-280