f07mathgrad_fall

f07mathgrad_fall - Review: Grad, etc. Pressure field Figure...

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Unformatted text preview: Review: Grad, etc. Pressure field Figure 1 shows a Control Volume or circuit placed in a pressure field p ( x, y ). To evaluate the pressure force on the CV, we need to examine the pressures on the CV faces. Pressure Field Pressures on faces of y Control Volume x p Figure 1: Pressure field and Control Volume. Pressure force infinitesimal rectangular CV Let us now assume the CV is an infinitesimal rectangle, with dimensions dx and dy . We wish to compute the net pressure force (per unit z depth) on this CV, F = ( p d vector n ) ds where ds is the CV side arc length, either dx or dy depending on the side in question. As shown in Figure 2, the pressures across the opposing faces 1,2 and 3,4 are related by using the local pressure gradients p/x and p/y . Face pressures Normal vectors Axis unit vectors i j x y dx dy 1 2 4 3 9 9 2 x dx p p + 9 9 2 p p + y dy 9 9 2 p y dy p 9 9 2 x dx p p p n Figure 2: Infinitesimal CV surface pressures and normal vectors....
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f07mathgrad_fall - Review: Grad, etc. Pressure field Figure...

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