1. Physics 211 Lecture 26 Today’s Concepts: A) Moving Fluids B) Bernoulli’s Equation Mechanics Lecture 26, Slide 1

2. This picture is A) Real B) Fake Clicker Question Mechanics Lecture 26, Slide 2

3. Atmospheric pressure = big force Vacuum gun demo: Mechanics Lecture 26, Slide 3

4. Clicker Question Through which hole will the water come out fastest? P  gyP  gy Mechanics Lecture 26, Slide 4 A B C

5. a.k.a. Pipe doesn’t leak Continuity Equation Mechanics Lecture 26, Slide 5 Flow Rate (volume/time) is the same everywhere

6. Continuity Equation Mechanics Lecture 26, Slide 6 We used the formula A1v1=A2v2, to figure out the speed of the water in the top pipe. It seems we ignored the fact that it was going straight up. Shouldn't gravity have affected it, making it go slower? No – height will change pressure but not speed… I'm not sure if I'm missing something obvious, but what causes the fluid to go up in the pipe? Difference in pressure (force)

7. 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 bigger B) It is the same C) It is smaller The same amount of water flows through every part of the pipe during an amount of time, so it will flow faster in the constriction CheckPoint Mechanics Lecture 26, Slide 7

8.  K = W TOT Mechanics Lecture 26, Slide 8

9. Remember Work – Kinetic Energy Eqn Mechanics Lecture 26, Slide 9 Vol

10. a.k.a. Energy Conservation (When height doesn’t change) Bernoulli’s Equation Mechanics Lecture 26, Slide 10

11. 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 bigger B) It is the same C) It is smaller A) The pressure is higher because there is less area for the water to travel through.. C) they're at the same height so P+.5pv^2 must always equal the same thing, and since v is greater in the constriction, pressure must be smaller.. B) It is always the same. Mechanics Lecture 26, Slide 11 CheckPoint

12. 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 12

13. Mechanics Lecture 26, Slide 13 Bernoulli’s Equation when height changes

14. 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) P L  2P R B) P L  P R C) P L  ½ P R D) The relative size of P L and P R depends on the speed of the flow. CheckPoint Mechanics Lecture 26, Slide 14 hLhL hRhR PLPL PRPR 0 Bernoulli’s Equation “Bent pipe was a little confusing.”

15. 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) P L  2P R B) P L  P R C) P L  ½ P R D) P L  P R  g  h R  h L  Clicker Question Mechanics Lecture 26, Slide 15 hLhL hRhR PLPL PRPR 0 Bernoulli’s Equation

16. 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) P L  2P R B) P L  P R C) P L  ½ P R D) P L  P R  g  h R  h L   1 / 2  v R 2  v L 2  Clicker Question Mechanics Lecture 26, Slide 16 hLhL hRhR PLPL PRPR 0 Bernoulli’s Equation

17. We just saw that P L  P R can be written in the following way: Is there any reason this has to mean P L  2P R or P L  P R or P L  ½ P R A) Yes B) No Clicker Question Mechanics Lecture 26, Slide 17 hLhL hRhR PLPL PRPR 0 Bernoulli’s Equation

18. 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) P L  2P R B) P L  P R C) P L  ½ P R D) The relative size of P L and P R depends on the speed of the flow. CheckPoint Mechanics Lecture 26, Slide 18 hLhL hRhR PLPL PRPR 0

19. Flow rate = A * v (units of m 3 /s) Mechanics Lecture 26, Slide 19

20. Mechanics Lecture 26, Slide 20

21. Volume = Flow rate x time time = Volume / Flow Rate Mechanics Lecture 26, Slide 21

22. same Mechanics Lecture 26, Slide 22

23. Mechanics Lecture 26, Slide 23

24. Assume the roof is flat. Bernoulli’s Equation Mechanics Lecture 26, Slide 24 Please explain the roof problem from the homework.