Active/Collaborative Learning Student Teams Integrating Technology Effectively Women and Minorities Assessment and Evaluation EC2000 Emerging Technology Foundation Coalition Curricula Concept Inventories
 
 
 
 
 
A Unified Framework for Engineering Science: Principles and Sample Curricula
 

Sophomore Engineering Curricula
Introduction  Conservation and Accounting Framework Curriculum Structure: Texas A&M four-course structure Curriculum Structure: Texas A&M Five-Course Structure
Curriculum Structure: Rose-Hulman Institute of Technology Sophomore Engineering Curriculum Example Problems

Student Performance/Faculty Reactions

Conclusions

 

Example 1: Water Hammer

Consider a tank filled with water of constant density r. The tank has a constant area A and a pipe at the bottom from which a flow rate of Q exits. The pressure at the bottom of the tank is P. For demonstration purposes, the exiting flow rate is given. The problem could also be solved by expressing a relationship between the pressure at the tank bottom and flow rate. The problem is to derive an equation for the height of fluid in the tank, see Figure 1.

  

Figure 1 - Water tank with water exiting at a rate of Q.

The process requires the identification of the following:

1.      a boundary,

2.      properties to count,

3.      the degrees of freedom,

4.      the order.

If the water motion is “well behaved” with no turbulence or velocity profile, the model has a single degree of freedom. All the water moves together. If 1 unit of mass is removed, the position of all other mass is determinable. The following model will assume one dof.

The properties that can be counted include:

·        mass, which can be determined by the height of the fluid in the tank,

·        energy, which can be identified by fluid height and velocity,

·        momentum, accounted by fluid velocity.

Since fluid position and fluid velocity are independent, the system is at maximum, second order. The conditions that allow velocity to be neglected are small Q and large A.

Suppose the fluid speed is neglected. The model will be order one, degree of freedom one. Since the number of given motions is equal to the dof, the problem only requires expressing a kinematical constraint. That is what the conservation of mass does. The model consists of writing the conservation for the only “important” property, mass, and is:

                                  (1)

Now suppose the fluid speed is significant. The degree of freedom is still one, but the order is two. The mass conservation is identical to the previous but now the energy and momentum need to be handled. The conservation of linear momentum in the vertical direction can be easily derived.  First from the free body diagram shown in Figure 2 ,figure ?, the vertical force from the gage pressure at the bottom of the fluid is .

Figure 2 Freebody of the Water in the Tank.

The gravity force is . The momentum of the fluid in the tank is

(students sometimes miss the ½ because they forget that they are computing the velocity of the center of mass of the fluid). With these expressions, the conservation of linear momentum says:

                                      (2)

Now consider what these say. Suppose the flow rate is held constant for a while, the rate of change of h is a constant so the pressure at the tank bottom is equal to the fluid weight. Now suppose the flow rate is suddenly stopped. In other words,  at t- and at t+, is discontinuous. When this happens equation 1 says (which was negative)  suddenly becomes zero, is discontinuous. This which means . Using this in the momentum equation (2) indicates that the pressure at the bottom of the tank suddenly jumps to for a very short time. Of course in the real world the pressure will not go to infinity because some of the fluid will leak, the container will expand slightly etc. but the pressure will be large. This large pressure for a short period is what is called water hammer. So what causes water hammer? Water hammer is caused by a sudden change in flow rate in a system where fluid momentum is not negligible.

What this example demonstrates is that (1) the conservation principles can derive the water hammer equations easily, (2) the use of degree of freedom helps to identify that the motion of the fluid height is directly related to the flow rate, (3) the use order helps to identify how many and what type of equations are required.

Before we leave this example, consider what conservation of momentum tells you in a system where the momentum and its change is insignificant. If the momentum and its change is insignificant, the term on the right of equation (2) is zero, hence:  in other words, the pressure equals the static fluid weight (obviously). The point here is that the conservation equations are always valid and when written they will tell you something. Because of this point, some of the authors make a habit of teaching students to always write every conservation equation for every problem (this is an exaggeration of course but it makes the point). Order however is a useful tool to help determine the number and type of differential equations that are required for the model. The number and type of differential equations is important to know from a system dynamics or control point of view.

Back

References

  1. Grinter, L.E. (Chair), Report on Evaluation of Engineering Education, American Society for Engineering Education, Washington, DC, 1955.
  2.   Harris, Eugene M. DeLoatch, William R. Grogan, Irene C. Peden, and John R. Whinnery, "Journal of Engineering Education Round Table: Reflections on the Grinter Report," Journal of Engineering Education, Vol. 83, No. 1, pp. 69-94 (1994) (includes as an Appendix the Grinter Report, issued in September, 1955).
  3. Glover, Charles, J., and Carl A. Erdman, "Overview of the Texas A&M/NSF Engineering Core Curriculum Development," Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 11-14 November 1992, pp. 363-367
  4. Glover, Charles J., K. M. Lunsford, and John A. Fleming, “TAMU/NSF Engineering Core Curriculum Course 1: Conservation Principles in Engineering,” Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 11-14 November 1992, pp. 603-608
  5. Glover, Charles J., K. M. Lunsford, and John A. Fleming, Conservation Principles and the Structure of Engineering, 3rd edition, New York: McGraw-Hill College Custom Series, 1992
  6. Pollock, Thomas C., “TAMU/NSF Engineering Core Curriculum Course 2: Properties of Matter,” Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 11-14 November 1992, pp. 609-613
  7. Pollock, Thomas C., Properties of Matter, 3rd edition, New York: McGraw-Hill College Custom Series, 1992
  8. Everett, Louis J., “TAMU/NSF Engineering Core Curriculum Course 3: Understanding Engineering via Conservation,” Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 11-14 November 1992, pp. 614-619
  9. Everett, Louis J., Understanding Engineering Systems via Conservation, 2nd edition, New York: McGraw-Hill College Custom Series, 1992
  10. Glover, Charles J. and H. L. Jones, “TAMU/NSF Engineering Core Curriculum Course 4: Conservation Principles for Continuous Media,” Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 11-14 November 1992 Conference, pp. 620-624
  11. Glover, C. J. and H. L. Jones, Conservation Principles for Continuous Media, 2nd edition, New York: McGraw-Hill College Custom Series, 1992
  12. Erdman, Carl A., Charles J. Glover, and V. L. Willson, “Curriculum Change: Acceptance and Dissemination,” Proceedings, 1992 Frontiers in Education Conference, Nashville, Tennessee, 11-14 November 1992, pp. 368-372
  13. B. A. Black, “From Conservation to Kirchoff: Getting Started in Circuits with Conservation and Accounting,” Proceedings of the 1996 Frontiers in Education Conference, Salt Lake City, Utah, 6-9 November 1996
  14. Griffin, Richard B., Louis J. Everett, P. Keating, Dimitris C. Lagoudas, E. Tebeaux, D. Parker, William Bassichis, and David Barrow, "Planning the Texas A&M University College of Engineering Sophomore Year Integrated Curriculum," Fourth World Conference on Engineering Education, St. Paul, Minnesota, October 1995, vol. 1, pp. 228-232.
  15. Everett, Louis J., "Experiences in the Integrated Sophomore Year of the Foundation Coalition at Texas A&M," Proceedings, 1996 ASEE National Conference, Washington, DC, June 1996
  16. Richards, Donald E., Gloria J. Rogers, "A New Sophomore Engineering Curriculum -- The First Year Experience," Proceedings, 1996 Frontiers in Education Conference, Salt Lake City, Utah, 6-9 November 1996
  17. Heenan, William and Robert McLaughlan, "Development of an Integrated Sophomore Year Curriculum,” Proceedings of the 1996 Frontiers in Education Conference, Salt Lake City, Utah, 6-9 November 1996
  18. Mashburn, Brent, Barry Monk, Robert Smith, Tan-Yu Lee, and Jon Bredeson, "Experiences with a New Engineering Sophomore Year,” Proceedings of the 1996 Frontiers in Education Conference, Salt Lake City, Utah, 6-9 November 1996
  19. Everett, Louis J., "Dynamics as a Process, Helping Undergraduates Understand Design and Analysis of Dynamics Systems," Proceedings, 1997 ASEE National Conference,
  20. Doering, E., “Electronics Lab Bench in a Laptop: Using Electronics Workbench to Enhance Learning in an Introductory Circuits Course,” Proceedings of the 1997 Frontiers in Education Conference, November 1997
  21. Cornwell, P., and J. Fine, “Mechanics in the Rose-Hulman Foundation Coalition Sophomore Curriculum,” Proceedings of the Workshop on Reform of Undergraduate Mechanics Education, Penn State, 16-18 August 1998
  22. Cornwell, P., and J. Fine, “Mechanics in the Rose-Hulman Foundation Coalition Sophomore Curriculum,” to appear in the International Journal of Engineering Education
  23. Cornwell, P. and J. Fine, “Integrating Dynamics throughout the Sophomore Year,” Proceeedings, 1999 ASEE Annual Conference, Charlotte, North Carolina, 20-23 June 1999
  24. Burkhardt, H. "System physics: A uniform approach to the branches of classical physics." Am. J. Phys. 55 (4), April 1987, pp. 344–350.
  25. Fuchs, Hans U. Dynamics of Heat. Springer-Verlag, New York, 1996.

Back

 

Pilihan Pasar Angka Lengkap di Bandar Togel Terpercaya Internasional

Kami adalah Bandar Togel Terpercaya unggulan dengan pilihan pasar angka yang paling lengkap. Kami telah menjalin kerjasama dengan penyedia pasar angka dari berbagai negara. Selain itu, situs ini juga diakui secara resmi sebagai otoritas dalam permainan angka online internasional, menjadikannya tempat terbaik bagi para penggemar permainan ini.

Pasaran Hong Kong dan Sydney selalu menjadi pilihan populer bagi pemain togel. Situs Togel online resmi ini menyediakan kedua pasaran tersebut dengan jaminan keamanan dan keadilan dalam setiap pengundian. Pemain dapat menikmati berbagai fitur menarik yang akan menambah pengalaman bermain.

Platform togel IDN menawarkan berbagai pasaran menarik, salah satunya adalah pasaran Macau yang dikenal dengan jackpot besar. Para pemain memiliki peluang memenangkan hadiah fantastis dengan mengikuti permainan ini. dengan sistem yang transparan dan layanan customer service yang selalu siap membantu, Situs Togel menjadikan pengalaman bermain lebih menyenangkan dan bebas dari kekhawatiran.

Kesalahan Umum yang Harus Dihindari Saat Bermain Togel 2D

Banyak pemain melakukan kesalahan dengan memasang taruhan terlalu besar atau mengikuti insting tanpa strategi yang jelas di Bo Togel Hadiah 2d 110rb. Penting untuk menghindari overbetting dan selalu bermain dengan anggaran yang sudah ditetapkan. Dengan begitu, pemain dapat menikmati permainan dengan aman tanpa mengalami kerugian besar.

Related Links:

Togel178

Pedetogel

Sabatoto

Togel279

Togel158

Colok178

Novaslot88

Lain-Lain

Partner Links