Application of partial derivatives

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  • #1
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sorry folks i dont even have an idea to this question`s solution so i hope u people may like to help me. i`m stuck to it since last week nd i hope its from partial derivative... plz suggest me a book or a hint or the solution.

Let a long circular cylinder of unit radius be placed in a large body of fluid flowing with uniform velocity, the axis of cylinder being perpendicular to the direction of flow. determine the steady flow.also show that the speed of the fluid at points on the cylinder surface is 2A|SinØ|.
 

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  • #2
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I would say your formula you are given is that the radius of the cylinder is say x2 + y2 = 1 (as it is a unit radius), and allow your function f(x,y) = x2 +y2 -1 = some constant C (as your Z value can be any value you want it to be as the cylinder extends in either direction of Z). So given this, you can solve for your gradient (which is the vector given by the partial derivatives). So partial f respect to x = 2x, partial f respect to y = 2y, so the gradient is given by the vector <2x,2y>. This vector would be equivalent to your uniform velocity vector (flow rate). After that I'm not really sure how to determine the exact velocity though.. that may start you?
 
  • #3
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i`ll try though i have only 1 day left to solve it.... thank you for the reply...
 

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