{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Problem 5.85

# Problem 5.85 - Problem 5.85[Difficulty 3 Given Find...

This preview shows page 1. Sign up to view the full content.

(a) Expression for circulation about a closed contour of height h and length L (b) Evaluate part (a) for h = b/2 and h = b (c) Show that the same result is obtained from area integral of Stokes Theorem (Eq. 5.14) Problem 5.85 [Difficulty: 3] Given: Velocity field for pressure-driven flow between stationary parallel plates Find: Solution: We will apply the definition of circulation to the given velocity field. s d V Governing Equations: (Definition of circulation) s d V dA V A (Stokes Theorem) Assumptions: (1) Steady flow 4 3 2 1 s d V s d V s d V s d V From the definition of circulation we break up the integral: dx b y b y U j dy i dx i b y b y U s d V 1 ˆ ˆ ˆ 1 The integrand is equal to: Therefore, the circulation is equal to: Γ 0 L x U 0 b 1 0 b d L 0 x U h b 1 h b d U L
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern