LectureExample_5-1

LectureExample_5-1 - Problem 5.2 Given: Velocity fields...

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Problem 5.2 [2] Given: Velocity fields Find: Which are 3D incompressible Solution: Basic equation: x u y v + z w + 0 = Assumption: Incompressible flow a) uxy , z , t , () y 2 2x z + = vxy , z , t , 2 y z x 2 y z + = wxy , z , t , 1 2 x 2 z 2 x 3 y 4 + = x , z , t , 2z y , z , t , x 2 z z , z , t , x 2 z Hence x u y v + z w + 0 = INCOMPRESSIBLE b) , z , t , x y z t = , z , t , x y z t 2 = , z , t , z 2 2 xt 2 yt = x , z , t , ty z y , z , t , t 2 x z z , z , t , zt 2 x Hence x u y v + z w + 0 = INCOMPRESSIBLE c) , z
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