P15_062 - 62. (a) The volume rate of ow is related to speed...

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62. (a) The volume rate of flow is related to speed by R = vA .Thu s , v 1 = R 1 πr 2 stream = 7 . 9cm 3 / s π (0 . 13cm) 2 =148 . 8cm / s=1 . 5m / s . (b) The depth d of spreading water becomes smaller as r (the distance from the impact point) increases due to the equation of continuity (and the assumption that the water speed remains equal to v 1 in this region). The water that has reached radius r (with perimeter 2 πr ) is crossing an area of 2 πrd . Thus, the equation of continuity gives R 1 = v 1 2 πrd = d = R 2 πrv 1 . (c) As noted above, d is a decreasing function of r . (d) At r = r J we apply the formula from part (b): d J = R 1 2 πr J v 1 = 7 . 9cm 3 / s 2 π (2 . 0 cm)(148 . 8cm / s) =0 . 0042 cm . (e) We are told “the depth just after the jump is 2 . 0 mm” which means d 2 =0 . 20 cm, and we are asked to Fnd v 2 . We use the equation of continuity: R 1 = R 2 = 2 πr J v 1 d J =2 πr 0 J v 2 d 2 where r 0 J is some very small amount greater than r J (and for calculation purposes is taken to be thesamenumer ica lva lue ,2 . 0 cm). This yields v 2 = v 1 µ d 1 d 2 = (148 . 8cm / s) µ 0 .
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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