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Unformatted text preview: across which fluid flows is the horizontal plane between the ball and the tank walls. On this part of the control-volume surface, the absolute velocity of the fluid and the control-volume velocity are u = 1 10 V b k and u cv = V b k 574 CHAPTER 6. CONTROL-VOLUME METHOD Also, the outer unit normal on this part of the control volume is n = k . Therefore, because the area between the tank and the sphere is the difference between the tank cross-sectional area, h 2 , and the area of the spheres projection on a horizontal plane, d 2 / 4 , we have 8 s 8 S u rel n dS = 88 A } 1 10 V b k ( V b k ) ] k dA = 11 10 V b w h 2 4 d 2 W Therefore, the mass-conservation equation simplifies to V b h 2 + 11 10 V b w h 2 4 d 2 W = 0 = 1 10 V b h 2 = 11 40 V b d 2 Solving for d , we find d = 2 h 11 = d = 0 . 34 h...
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This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.
- Spring '06