**Unformatted text preview: **the horizontal part of the tube into elements of thickness dr ; the pressure difference between the sides of this piece is dr r dp ) ( 2 = (see Problem 14.78), and integrating from , 2 gives to 2 2 l p l r r ρϖ = ∆ = = giving the same result. c) At any point, Newton’s second law gives pAdla dpA = from which the area A cancels out. Therefore the cross-sectional area does not affect the result, even if it varies. Integrating the above result from 0 to l gives pal p = ∆ between the ends. This is related to the height of the columns through y pg p ∆ = ∆ from which p cancels out....

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