1. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 1 Science A 52 Lecture 12 March 15, 2006 Energy Equation for flowing Fluids Per capita US Energy Consumption from 1850 to 2000 Examples of steam engines both stationary and locomotive A few of Watt’s problems with the kinematics of connecting his steam engine to other things

2. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 2 Hints to understanding the amount of power available to water turbines Basic flow energy equations generally give insight into the maximum amount of energy available without frictions The energy equation for flowing fluids can be derived Using simple algebraic calculations. So let us try doing it together, working from PowerPoint slides and at the board.

3. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 3

4. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 4 The first step

5. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 5 The Pressure Work at Station 1

6. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 6 All together

7. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 7 Work done by the pressure at Station 2

8. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 8 Work done by the pressure at Station 2

9. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 9 Total work done on the system

10. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 10 Energy Flowing into the System

11. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 11 Energy out minus Energy in

12. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 12 The Full Energy Equation

13. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 13 Maximum Power from Turbine

14. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 14 Force and Change in Momentum

15. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 15 Newton’s Law of Motion and a System of Particles We can apply this Law of Motion to a fixed system of particles. We can calculate the Momentum M of a group of fluid particles at time t=0, and then calculate the momentum M(t=∆t). We need to look at a convenient group of particles to Tell us the force on the shaped pipe in the last slide.

16. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 16 Selecting the group of particles At t=0, the selected group is all of Region 1, and 2 At t=∆t, the same group of particles has flowed to Region 2 and 3. Let M 1 (0)+M 2 (0) = momentum of the particles in Regions 1 and 2 Let M 2 (∆t)+M 3 (∆t) = momentum of the particles then in Region 2 and 3 at t=∆t.

17. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 17 {M 2 (∆t)+M 3 (∆t)} - {M 1 (0)+M 2 (0)} = F ∆t But M 2 (∆t) = M 2 (0) : see from the sketch above that this is true. M 3 (∆t) - M 1 (0) = F ∆t

18. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 18 M 3 (∆t) - M 1 (0) = F ∆t x M 3 (∆t) M 3 (∆t) = M 1 (0) = F = Positive x direction

19. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 19 Summary The available power is essentially = The passage ways in the turbine have to be curved to guide the flow and to put force on the rotating blades and direct the flow downward. The shape of the passages Is critical to achieving high power recovery. Maximum power in the 1850 was about 85%, now it is likely in the 90+ % of maximum. Waterwheels were about 60 to 70% efficient

20. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 20 US Per Capita Energy Consumption Data for the years 1850 to 1950 called series 1 see J. Frederic Dewhurst and Associates, America’s Needs and Resources: A New Survey, (The Twentieth Century Fund, New York, 1955), pp. 1114. Data for years 1950 to 2000 called series 2 on the charts see UCRL-ID-129990-00,U.S. Energy Flow -2000,Gina V. Kaiper, Feb. 2002

21. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 21 US Population from the Census Bureau In the graph that follows human energy sources - estimated in Reference 1- has been eliminated in the total energy consumed in the US. All other sources have been included.

22. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 22

23. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 23 Why did per capita consumption rise during various years? The first bump up was in 1880-90 Then 1900-10 Then dips in 1930-1940 Then up from 1940-1970 Nearly flat from 1970-2000

24. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 24

25. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 25

26. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 26 Back to our Total Energy Slides Coal became a significant fuel crossing wood in BTUs used between 1880 and 1890 By 1910 oil became a significant energy fuel From 1930 through 1940 there was the great depression From 1940-45 was WWII 1950-70 the great post war economic expansion 1973 - The first energy crisis for the US

27. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 27

28. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 28 US Per Capita Energy Consumption Surprises From 1970 to 2000 per capital energy consumption is nearly flat. Simple energy conservation steps has lead to leveling demand Domestic lighting has improved - look at the touchier lamps in your rooms in the Houses

29. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 29 US per Capita Consumption - continued The fluorescent torchere used at Harvard were designed by Dr. Linsey Marr when she was an undergraduate at Harvard The lamp has the lumen output of the 300 watt halogen torchere and uses just 1/4 the electrical power Many other consumer items have been improved - such as home refrigerators. They use less that half the power of those of 20 years ago.

30. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 30 Turning Now to Watt’s Steam Engines Let us look at a few of the mechanical problems Watt followed Newcomen in using a beam machine Let us look at the Newcomen machine to see some of the mechanical problems

31. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 31

32. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 32 One of the Problems Look at the chains from the beam to the pump and the steam piston A chain connection means that only tensions can be transmitted The beam is constructed such that the chain at the same point in space- the beam is really a portion of the arc of a circle This geometry keeps the pump “rod” and the piston “rod” vertical and moving along a vertical line Two problems - 1) the chain can only transmit tension, and 2) having a chain allows the “rods” to remain vertical

33. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 33 More on Problems The first steam engines of Watt’s also pumped water His Customers wanted rotary motion too not just linear motion The simple crank was patented, so Watt wanted to invent another way to convert linear motion into rotary motion

34. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 34 Diagrams on the Chalk Board Figures on the Board is of a coin rolling without slip around another similar coin that is fixed in place The rolling coin is shown in four positions

35. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 35 Is there a way to determine and expression for the rotation for two gears of any diameter? ! Yes there is a way and it involves computing the velocity at the point of contact.

36. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 36 Again this will be done at the board since it is very difficult to get everything into a single figure.

37. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 37 A double Acting Steam Cylinder http://travel.howstuffworks.com/steam1.htmhowstuffworks.com/steam1.htm

38. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 38 Useful Web sites http://inventors.about.com/gi/dyn amic/offsite.htm?site=http://www.h owstuffworks.com/steam.htm http://www.brockeng.com/mecha nism/Watt.htmhttp://www.brockeng.com/mecha nism/Watt.htm http://www.keveney.com/Engines.htmlhttp://www.keveney.com/Engines.html http://www.nmes.org/

39. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 39 The End

40. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 40

41. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 41 The Important Dimensions of Piston and Slider b = the length of crank arm C = separation of the slide block and the center of the flywheel a = the third side of the triangle

42. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 42 The length C gives us the piston motion with time

43. Spring 2006  Harvard Science A 52 FHA+MBM Lecture 12 43 Separation of the Piston “C” /Crank”B”