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![[Post New]](/templates/default/images/icon_minipost_new.gif) 7 Jul 2007 21:14:29 IST
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Flow velocity of river increases linearly with distance 'r' from bank and has maximum value ' v ' 'in middle.Velocity at bank is zero. A boat can move with speed 'u ' in still water.It moves in the river such that it's velocity is always perpendicular to flow of current.Find the distance along bank through which boat is carried away by current while crossing the river. Width of river is' d '.
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7 Jul 2007 21:30:39 IST
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velocity of current at a distance r frm bank...= 2rv/D..
time taken by boat 2 cross river = D/u...
consider a small elemnt of width dr in which portion the speed of current can b assumed 2 b a constant..let the boat take time dt 2 cross dis dr distance..
so, (2rv/D) * dt = elemental drift.. now time dt 2 cross dis element = dr/u..
so elemental drift = (2rv/D) * (dr/u) ....integrate wid distance limits going frm 0 to D/2
ur integrating for half the distance ...frm bank 2 midpoint..the other half will have same drift...
so net drift = vD/2u
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11 Jul 2007 21:02:32 IST
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Very good answer naveen. Just want to correct for one thing which you know but is not clear from first part of your answer. V(r) = 2rv/D if r< D/2 else V(r) = 2v-2rv/D
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Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi |
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