Problem 6.1 - Problem 6.1 [Difficulty: 2] Given: Velocity...

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Problem 6.1 [Difficulty: 2] Given: Velocity field Find: Acceleration of particle and pressure gradient at (1,1) Solution: NOTE: Units of B are s -1 not ft -1 s -1 Basic equations For this flow uxy , () A y 2 x 2 Bx = vxy , 2 A x y By + = a x u x u v y u + = Ay 2 x 2 x 2 x 2 2A x y + y 2 x 2 + = a x B2 A x + A x 2 + 2 + = a y u x v v y v + = 2 x 2 x x y + x y + y x y + + = a y A x + B y x y + y Ax 2 y 2 + = Hence at (1,1) a x 12 1 1 + 1 s 11 2 + 2 + × ft s = a x 9 ft s 2 = a y 1 1 + 1 s 21 1 1 + × ft s 1 1 s 2 1 2 + × ft s = a y 7 ft s 2 = aa x 2 a y 2 + = θ atan a y a x = a 11.4 ft s 2 = θ 37.9 deg = For the pressure gradient
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