To determine The resultant force acting on the triangular plate A and the location of the center of pressure. Explanation Draw the cross section of one half of the triangular plate A as shown in Figure (1). Calculate the equation of the triangular plate. y 1.8 = 1 − x 1 x = ( 1 − 0.556 y ) m Draw the cross section of the triangular plate and show the differential element as in Figure (2). Calculate the pressure acting on the plate ( p ). p = ρ w g ( h − y ) p = 1 , 000 × 9.81 ( 3.2 + y ) N/m 2 = 9 , 810 ( 3.2 + y ) N / m 2 (I) Calculate the area of the differential element ( dA ). d A = ( x + x ) d y = 2 x d y d A = 2 ( 1 − 0.556 y ) d y = ( 0.75 − y ) d y (II) Determine the force ( dF ) acting on the differential element. d F = p d A d F = 9 , 810 ( 3.2 + y ) × 2 ( 1 − 0.556 y ) d y = 19620 ( − 0.556 y 2 − 0.78 y + 3.2 ) d y (III) Determine the resultant force acting on the triangular plate by integrating the force from 0 to 1.8 m. F R = ∫ 0 1.8 19620 ( − 0.556 y 2 − 0.78 y + 3.2 ) d y = 1962 [ − 0

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2, Problem 78P

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The resultant force acting on the triangular plate A and the location of the center of pressure.

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Chapter 2, Problem 77P

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