Midterm Exam 2004 solutions.doc

Answer b is also incorrect refer to table 17 1 which

Info icon This preview shows pages 11–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Answer b is also incorrect. Refer to Table 1.7-1 which demonstrates that the direction of the momentum flux is the same as the direction of the velocity vector. Since the surface itself can be arbitrarily selected, the velocity vector, and hence the momentum flux may not be perpendicular to the surface. Answer c is correct since it is the definition of momentum flux. Answer d is also correct. The nonlinear terms (on the left hand side of the momentum equations) have the form u u , and this is a nonlinear term. Therefore, both c and d are true, so the correct answer is e. 18. The momentum equation used in the book and typically used in fluid mechanical applications: a. is written in terms of a Lagrangian frame of reference. b. is written in terms of an Eulerian frame of reference. c. is linear in all practical applications. d. contains 3 unknown variables. 11
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Steven A. Jones BIEN 501 Physiological Modeling Midterm Exam April 7, 2004 e. none of the above. In solid mechanics, the equations are typically written in a Lagrangian frame of reference, where the coordinate system follows the motion of materials. A classic example is the equation for a falling body 2 2 1 0 at vt x x . Note that the coordinate x is chaging in time. In fluid mechanics, however, the equations are written with respect to a stationary coordinate system and measurements are made at a point in space. This frame of references is the reason for the use of the substantial derivative rather than the time derivative in the momentum equations. The momentum equation is certainly not linear in all practical applications. It is inherently non- linear, but sometimes reduces to a linear equation under special circumstances. The momentum equation contains 4 unknown variables. In Cartesian coordinates these are x v , y v , z v , and p . Therefore the correct answer is b. 19. The expression u a. is the continuity equation for incompressible flow. b. is a single equation. c. involves 3 unknown variables. d. contains y v y as one term. e. all of the above. I confess, this is another mistake on my part. The statement of the equation should have been, “The expression 0 u ….” In this case, it is the continuity equation for incompressible flow, and it is a single equation since the dot product of the vector and the vector u yields a scalar. (The expression contrasts with that in question 20 below, where the vector formulation of the momentum equation is three separate equations, one for x v momentum, one for y v momentum, and one for momentum). It also involves 3 unknown variables, which are x v , y v , and z v . It also includes the term y v y . Therefore, the correct answer is e. However, since some of you may have been confused by my suggesting that u is a complete equation, I accepted also either answer c. or answer d.
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern