73_Problem CHAPTER 9

73_Problem CHAPTER 9 - PROBLEM 9.65 Show that the system of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PROBLEM 9.65 Show that the system of hydrostatic forces acting on a submerged plane area A can be reduced to a force P at the centroid C of the area and two couples. The force P is perpendicular to the area and is of magnitude sin PA y γ θ = , where is the specific weight of the liquid, and the couples are ( ) sin xx I ′′ = Mi and ( ) sin yx y I = Mj , where xy I xy dA = (see Sec. 9.8). Note that the couples are independent of the depth at which the area is submerged. SOLUTION The pressure p at an arbitrary depth ( ) sin y is ( ) sin py = so that the hydrostatic force dF exerted on an infinitesimal area dA is ( ) sin dF y dA γθ = Equivalence of the force P and the system of infinitesimal forces dF requires :s i n s i n FP d F y d
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online