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Unformatted text preview: integral is: ( 29 n U AU y Uy=U in the y direction. This quantity is positive in accordance with the sign convention shown to the left of the figure. Uy=Ucos( ). Now examine the term ( 29 n U : This is the dot product of two vectors. First notice that U and n are in the opposite direction, this gives the minus sign and tells us that the flux is into the control surface. The dot product asks us to find the component of the vector U in the direction of n, which is Usin( ). Note that the term ( 29 n U is the same for both the x and the y directions. Combining these, we get the y-component of the momentum flux across this surface: ( 29 cos sin 2 A U-x U n A y The x-component of the momentum flux across this surface is: ( 29 2 2 sin A U-To find the resultant momentum flux, we could that the square root of the sum of the squares of each of these quantities....
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- Spring '11