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Unformatted text preview: 4. The Euler equation is u t + ( u ) u =-1 p, where u = ( u,v,w ) is the velocity and p the pressure. Write out the second component of the Euler equation in components. 5. Simplify (i) ijk ijm ; (ii) ijk ijk . 6. Demonstrate that for ( x ), a scalar function of position = 0 7. Prove the vector identity, for vector eld u ( x ) and v ( x ), ( u v ) = u ( v )-v ( u ) + ( v ) u-( u ) v 8. Show that for a vector eld u ( x ) u ( | u | 2 / 2) = u ( u ) u 9. For each of the following functions, ( x ), nd and 2 4 using sux notation and the summation convention. (i) = f ( r ); f is an arbitrary scalar function (ii) = a x /r 3 , where a is a constant vector and r 2 = x x ....
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- Fall '11