Assume that the pressure in a volume of air can be expressed to first order in a
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Assume that the pressure in a volume of air can be expressed to first order in a local coordinate system (x, y, z) as p = p0 + f x + O(x2, y2, xy, . . .). Show from the balance of forces on a small volume element dV that the force per unit volume is f in the −x-direction. Using the fact that the coordinate system can be chosen arbitrarily, show that more generally f p = −∇P.
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