# Chall_3 - Challenge Problem 3(OPTIONAL Name 1 Consider a real fluid(Q v 0 of constant density Use the Navier-Stokes Equations to show that J K K K

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Challenge Problem 3 (OPTIONAL) Name: ____________________ 1. Consider a real fluid ( Q v 0 ) of constant density. Use the Navier-Stokes Equations to show that K Vd l = ± ² ×× V ) ¸ n d S + ²¸ ¸ ( Z ˆ l (1) d * = d ¨ v JK K ¨ ¨ K K ¨ v 2 K C A C dt dt where C is a closed curve fixed in space and A is any surface bounded by C . K K K K K K V ¸ Hint : Use the identity ( V ¸² ) V =×+ ² ( 1 V V ) . 2 2. A real, constant density fluid flows over a thin flat plate placed in a free stream of K velocity V = U i ˆ , creating a boundary layer. Assume that the flow is steady. Consider a rectangular curve fixed with respect to the plate and boundary layer as shown: y h U x 0 p curve C boundary layer 1 p 2 p 1 x 2 x , s s xp The point x at the leading edge of the plate is a stagnation point where the stagnation s pressure is p s . The pressure at point x is p 1 . Point x is assumed to be far enough 1 2 downstream in the boundary layer that p 2 equals the free stream pressure p 0 .

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## This note was uploaded on 02/27/2012 for the course MECHANICAL 2.20 taught by Professor Dickk.p.yue during the Spring '05 term at MIT.

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Chall_3 - Challenge Problem 3(OPTIONAL Name 1 Consider a real fluid(Q v 0 of constant density Use the Navier-Stokes Equations to show that J K K K

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