HW_15_Soln

# HW_15_Soln - The x-velocity component of a steady 2D...

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Page 1 of 1 The x -velocity component of a steady, 2D, incompressible flow is given by: x uy x =− Determine the most general velocity component in the y -direction for this flow. SOLUTION: Consider the continuity equation: 0 y x u u xy += ∂∂ (1) () 1 y x u u yx x = Integrate u y with respect to y . y f x =+ (2) where f ( x ) is an unknown function of x . Double check: 1 x u xx = (3) 1 y u yfx yy = ⎡⎤ ⎣⎦ (4) 11 0 y x u u ⇒+= + = OK! (5)

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Page 1 of 1 A velocity field for an incompressible flow is given by 22 ˆˆ ˆ (2 ) ( 2 ) ( 2 2 ) x zx y zz x z y z =− + + + ui j k Is this flow physically possible? SOLUTION: Does the given velocity field satisfy the continuity equation? 0 y x z u u u xyz ++= ∂∂∂ (1) Using the given velocity field: () x u x xx = ∂∂ 2 y u x yz x yy =+ = 2 2 2 2 z u z y x y = Substitute into Eqn. (1). 22222 2 0 y x z u u u zxzxy y + + = Hence, the given flow field is not physically possible since it does not satisfy the continuity equation.
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HW_15_Soln - The x-velocity component of a steady 2D...

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