Explanation Given information: The depth of the water is d = 18 in . The dimension of the square plate is 9 × 9 in . Assumption: Apply the sign convention for calculating the equations of equilibrium as shown below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and the downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counterclockwise moment as positive. Calculation: Calculate the pressure on the valve ( p ) as shown below p = γ h Here, γ is the unit weight of water. Calculate the width of the loading ( w ) as shown below. w = 9 p Substitute γ h for p . w = 9 γ h Sketch the Free Body Diagram as shown in Figure 1. Refer to Figure 1. Calculate the width of loading acting on the valve as shown below. For the loading P I : w 1 = 9 γ ( d − 9 ) Substitute 18 in . for d . w 1 = 9 γ ( 18 − 9 ) = 81 γ For the loading P I I : w 2 = 9 γ d Substitute 18 in . for d . w 2 = 9 γ × 18 = 162 γ Calculate the loading ( P I ) as shown below. P I = 1 2 × 9 w 1 Substitute 81 γ for w 1

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Chapter 5.3, Problem 5.85P

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Find the distance h from the bottom of the valve to the pivot A.

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Chapter 5.3, Problem 5.84P

Chapter 5.3, Problem 5.86P

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Vector Mechanics for Engineers: Statics, 11th Edition

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Find the distance h from the bottom of the valve to the pivot A .

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Find the distance h from the bottom of the valve to the pivot A.

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