To determine Determine the fluid pressure will give the gate an initial counter clockwise angular acceleration. Explanation Show the free body diagram of the hydraulically operated gate as in Figure (1). Express the cross-sectional area of the piston. A = π 4 d p 2 (I) Here, piston diameter is d p . Express the mass of the gate. m = W g (II) Here, weight of the gate is W and acceleration due to gravity is g . Express the mass moment of inertia of the gate about O . I O = m k O 2 (III) Here, radius of gyration is k O . Refer Figure (1), and take moment about O . ∑ M O = I O α ( p A sin θ ) ( 6 in . ) + ( p A cos θ ) ( 18 in . ) = I O α (IV) Here, angular acceleration of the gate is α , fluid pressure of the gate is p , area of the piston is A and the angle is θ . Conclusion: Substitute 2 in . for d p in Equation (I). A = π 4 ( 2 in . ) 2 = 3.14 in . 2 Express the value of θ from Figure (1). tan θ = 48 in . 14 in . θ = 90 ° − tan − 1 ( 3.4286 ) = 16.26 ° Substitute 500 lb for W and 9 .81 m / s 2 for g in Equation (II). m = 500 lb 9 .81 m / s 2 = 15.53 lb ⋅ sec 2 / ft Substitute 15

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 6.4, Problem 35P

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Determine the fluid pressure will give the gate an initial counter clockwise angular acceleration.

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Chapter 6.4, Problem 34P

Chapter 6.4, Problem 36P

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