To determine The height of water point B such that there is no seepage at point D . Explanation Given: The height of point C from bottom ( h C ) is 8 ft. The base distance between point C and point D ( b D ) is 6 ft. The unit weight of water ( γ w ) is 62.4 lb / ft 3 . The height of water from point A to C ( h A C ) is 4 ft. The width of the gate ( b ) is 8 ft. The height of water at point A from ground level ( h A ) is 12 ft. The weight of the plate ( W ) is 50 × 10 3 lb . Calculation: Calculate the length of the plate CD ( L C D ) . L C D 2 = h C 2 + b D 2 L C D 2 = ( 8 ft ) 2 + ( 6 ft ) 2 L C D = 10 ft Draw the cross section of the plate at CD and mark the level of water at B as shown in Figure (1). Calculate the equation for the level of water at B . x 10 = h 8 x = 5 4 h Here, the length of plate submerged with water is x and the height of water at point B is h . Calculate the intensity of load at point C due to point A ( w 1 ) . w 1 = γ w h A C b w 1 = 62.4 lb / ft 3 × 4 ft × 8 ft = 1 , 996.8 lb / ft Calculate the intensity of load at ground level due to point A ( w 2 ) . w 2 = γ w h A b w 2 = 62.4 lb / ft 3 × 12 ft × 8 ft = 5 , 990.4 lb / ft Calculate the intensity of load at ground level due to point B ( w 3 ) . w 3 = γ w h B b w 3 = 62.4 lb / ft 3 × h × 8 ft = 499.2 h lb / ft Here, the height of water at point B from ground level ( h B ) is h . Calculate the resultant force ( F 1 ) due to load w 1 . F 1 = w 1 L C D F 1 = 1 , 996.8 lb / ft × 10 ft = 19 , 968 lb Calculate the resultant force ( F 2 ) due to load w 2

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2, Problem 92P

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