Explanation Given information: The arbitrary depth is d = y sin θ Calculation: Calculate the moment of inertia about x axis as follows: I x = ∫ y 2 d A Calculate the moment of inertia about x axis as follows: I y = ∫ x y d A Find the pressure ( p ) at an arbitrary depth as shown below: p = γ ( y sin θ ) Find the hydrostatic force ( d F ) exerted on infinitesimal area as follows: d F = ( γ y sin θ ) d A Find the force P on the system as follows. P = ∫ d F Substitute ( γ y sin θ ) d A for d F . P = ∫ ( γ y sin θ ) d A = γ y ¯ sin θ ∫ d A = γ A y ¯ sin θ Apply the Equivalence of the force and couple and the system of infinitesimal hydrostatic force requires as follows. Summation of moment about x axis. ∑ M x = 0 − y ¯ P − M x ′ = ∫ ( − y d F ) Substitute ( γ y sin θ ) d A for dF . y ¯ P − M x ′ = − ∫ y ( γ y sin θ ) d A = − γ sin θ ∫ y 2 d A = − ( γ sin θ ) I x Substitute γ A y ¯ sin θ for P and I x for y 2 d A

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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ISBN: 9781260916942

Author: BEER

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Chapter 9.2, Problem 9.65P

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Show that the system of hydrostatic force acting on P is perpendicular to the area and magnitude and couple force of the system.

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Chapter 9.2, Problem 9.64P

Chapter 9.2, Problem 9.66P

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VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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Show that the system of hydrostatic force acting on P is perpendicular to the area and magnitude and couple force of the system.

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Show that the system of hydrostatic force acting on P is perpendicular to the area and magnitude and couple force of the system.

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