To determine The horizontal and vertical component of resultant force the water exerts on plate AB and BC . Explanation Given: Height of point B from point A ( h B ) is 2 m. Width of the plate ( b ) is 1.5 m. Radius of the quadrant ( r ) is 2 m. Density of water ( ρ w ) is 1000 kg / m 3 . Acceleration due to gravity ( g ) is 9.81 m / s 2 . Calculation: Draw the free body diagram of plate AB as in Figure (1). Determine the intensity of distributed load at point B for plate AB ( w B ) . w B = ρ w g h B b w B = 1 , 000 kg / m 3 × 9.81 m / s 2 × 2 m × 1.5 m = 29 , 430 N / m = 29.43 kN / m Determine the horizontal component of resultant force ( F h ) . F h = 1 2 w B h B F h = 1 2 × 29.43 kN / m × 2 m = 29.4 kN Thus, horizontal component of resultant force the water exerts on plate AB is 29.4 kN . Determine the length of point B from point A ( l B ) . tan θ = h B l B l B = h B tan θ l B = 2 m tan 45 ° = 2 m Determine the volume ( V ) of plate AB . V = 1 2 × l B × h B × b V = 1 2 × 2 m × 2 m × 1.5 m = 3 m 3 Determine the vertical component of resultant force ( F v ) . F v = ρ w g V F v = 1 , 000 kg / m 3 × 9

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2, Problem 17FP

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The horizontal and vertical component of resultant force the water exerts on plate AB and BC.

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Chapter 2 Solutions

Fluid Mechanics (2nd Edition)

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