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# p0390 - 348 CHAPTER 3 EFFECTS OF GRAVITY ON PRESSURE 3.90...

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348 CHAPTER 3. EFFECTS OF GRAVITY ON PRESSURE 3.90 Chapter 3, Problem 90 The most important fact to note about this problem is the role played by the ambient pressure, p a to the right and p b to the left, in the overall force on a surface. Because we have subtracted the ambient pressure from the pressure in the liquid, the total force on a surface is the computed hydrostatic force plus the force from the ambient pressure. For the problem at hand, the forces on the gate are as shown in Figure 3.70. Figure 3.70: Storage-tank forces and moment arms. Since the gate is rectangular, the hydrostatic forces are given by F f = ρ gA f z f and F r = ρ gA r z r Since the gate is 6 L wide (out of the page), the areas and centroids are A f = 12 L 2 , A r = 24 L 2 , z f = L, z r = 2 L Therefore the hydrostatic forces from the left and right sides of the gate are F f = 12 ρ gL 3 and F r = 48 ρ gL 3 Since the ambient pressure acts over the entire surface of the gate, denoting the contribution from the left by F b and from the right by F a , we have F

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p0390 - 348 CHAPTER 3 EFFECTS OF GRAVITY ON PRESSURE 3.90...

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