Explanation Given: The dam is inclined at an angle of 30 ° The shape of the dam is isosceles trapezoid with 100 ft wide at the top, 50 ft wide at the bottom, and 70 ft slant height. Calculation: Draw the shape of the dam as shown in Figure 1. Refer to Figure 1. Calculate the height of the dam: cos 30 ° = h 70 h = 70 cos 30 ° = 60.62 = 15 19 Calculate the width of the trapezoid w : w = 50 + 2 a (1) Here, a is length. Calculate the value of a using Figure 1: 25 h = a h − x a = 25 ( h − x ) h Substitute 25 ( h − x ) h for a in Equation (1). w = 50 + 2 [ 25 ( h − x ) h ] = 50 + 2 ( 25 h − 25 x h ) = 50 + 50 h − 50 x h = 50 + 50 h h − 50 x h = 50 + 50 − 50 x h = 100 − 50 x h Draw the triangle as shown in Figure 2. Refer to Figure 2. Calculate the z value: cos 30 ° = d x z 3 2 = d x z z = 2 d x 3 Consider the weight density of water as δ = 62.5 lb/ft 3 . Calculate the hydrostatic pressure on the dam when full of water as follows: P = δ x Calculate the hydrostatic area on the dam when full of water as follows: A = w z (2) Substitute ( 100 − 50 x h ) for w and 2 d x 3 for z in Equation (3). A = ( 100 − 50 x h ) ( 2 d x 3 ) = ( 200 3 − 100 x h 3 ) d x Calculate the hydrostatic force on the dam when full of water: F = ∫ a b P A (3) Substitute 0 for a , h for b , δ x for P and ( 200 3 − 100 x h 3 ) d x for A in Equation (4)

8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 8.3, Problem 16E

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To find: The hydrostatic force on the dam when full of water.

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Chapter 8.3, Problem 15E

Chapter 8.3, Problem 17E

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The hydrostatic force on the dam when full of water.

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