Classical MechanicsLecture 26

Today’s Concepts:A) Moving FluidsB) Bernoulli’s Equation

Mechanics Lecture 26, Slide 1

This picture isA) Real B) Fake

Clicker Question

Mechanics Lecture 26, Slide 2

Clicker Question

Through which hole will the water come out fastest?

P gy

Mechanics Lecture 26, Slide 3

A

B

C

Water flows through a pipe that has a constriction in the middle as shown. How does the speed of the water in the constriction compare to the speed of the water in the rest of the pipe?

A) It is biggerB) It is smallerC) It is the same

Water is incompressible so when it goes through the constriction the water has to speed up in order to squeeze all the water through

CheckPoint

Mechanics Lecture 26, Slide 4

Water flows through a pipe that has a constriction in the middle as shown. How does the pressure of the water in the constriction compare to the pressure of the water in the rest of the pipe?

A) It is biggerB) It is smallerC) It is the same

CheckPoint

Mechanics Lecture 26, Slide 5

Water flows through a pipe that has a constriction in the middle as shown. How does the pressure of the water in the constriction compare to the pressure of the water in the rest of the pipe?

A) It is biggerB) It is smallerC) It is the same

A) because it's being forced through a smaller pipe it has greater pressure.

C) Since the fluid is all at the same height the sum (P + .5pv²) is constant throughout the pipe. The velocity is greater in the constriction, so the pressure there must be smaller.

B) Pressure must be the same throughout the pipe.

Mechanics Lecture 26, Slide 6

CheckPoint

Clicker Question

Two empty pop cans are placed about ¼” apart on a frictionless surface. If you blow air between the cans, what happens?

A) The cans move toward each other. B) The cans move apart.C) The cans don’t move at all.

Blowing air

Mechanics Lecture 26, Slide 7

Water flows from left to right along a pipe as shown. The right end of the pipe is twice as high as and also has four times the area of the left end. Which of the following statements best relates the pressures at the ends of the pipe?

A) PL 2PR

B) PL PR

C) PL ½ PR

D) The relative size of PL and PR depends on the speed of the flow.

CheckPoint

Mechanics Lecture 26, Slide 9

hL

hR

PL

PR

0

Bernoulli’sEquation

RRRLLL ghvPghvP 22

2

1

2

1

Suppose the water isn't moving. The right end of the pipe is twice as high as and also has four times the area of the left end. Which of the following statements best relates the pressures at the ends of the pipe?

A) PL 2PR

B) PL PR

C) PL ½ PR

D) PL PR g hr hL

Clicker Question

Mechanics Lecture 26, Slide 10

hL

hR

PL

PR

0

Bernoulli’sEquation

2 21 1

2 2L L L R R RP v gh P v gh

Water flows from left to right along a pipe as shown. The right end of the pipe is twice as high as and also has four times the area of the left end. Which of the following statements best relates the pressures at the ends of the pipe?

A) PL 2PR

B) PL PR

C) PL ½ PR

D) PL PR g hR hL 1/2vR2 vL

2

Clicker Question

Mechanics Lecture 26, Slide 11

hL

hR

PL

PR

0

Bernoulli’sEquation

2 21 1

2 2L L L R R RP v gh P v gh

We just saw that PL PR can be written in the following way:

Is there any reason this has to mean PL 2PR or PL PR or PL ½ PR

A) YesB) No

Clicker Question

Mechanics Lecture 26, Slide 12

hL

hR

PL

PR

0

Bernoulli’sEquation

2 21 1

2 2L L L R R RP v gh P v gh

22

2

1RLLRRL vvhhgPP

Water flows from left to right along a pipe as shown. The right end of the pipe is twice as high as and also has four times the area of the left end. Which of the following statements best relates the pressures at the ends of the pipe?

A) PL 2PR

B) PL PR

C) PL ½ PR

D) The relative size of PL and PR depends on the speed of the flow.

CheckPoint

Mechanics Lecture 26, Slide 13

hL

hR

PL

PR

0

22

2

1RLLRRL vvhhgPP