Problem 5.72

# Problem 5.72 - y d A 2 x d 2 x a 2 y c 2 y d 2 x b 2 x c 2...

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Circulation about the unit square shown above. Problem 5.72 [Difficulty: 2] Given: Velocity field for flow in a rectangular corner as in Example 5.8. Find: Solution: We will apply the definition of circulation to the given velocity field. s d V Governing Equation: (Definition of circulation) da cd bc ab s d V s d V s d V s d V From the definition of circulation we break up the integral:   Aydy Axdx j dy i dx j Ay i Ax s d V ˆ ˆ ˆ ˆ The integrand is equal to: Therefore, the circulation is equal to: Γ x a x d x A x d y d y c y A y d x c x b x A x d y b y a y A y
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Unformatted text preview: y d A 2 x d 2 x a 2 y c 2 y d 2 x b 2 x c 2 y a 2 y b 2 Γ 1 2 0.3 1 s 2 2 1 2 2 2 1 2 1 2 2 2 1 2 2 2 m 2 Γ m 2 s This result is to be expected since the flow is irrotational and by Stokes' theorem, the circulation is equal to the curl of the velocity over the bounded area (Eqn. 5.18)....
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